I am pasting this sentence here: "Louvri fèy zòrèy nou pou n manyè tande lè m ap pale." What is "fey" and "manye" here. I do know both words, but don't understand them here.

fèy (leaf) means flap here.
manyè → at least see the link for "manyè"

Louvri fèy zòrèy nou pou n manyè tande lè m ap pale
Open the flap of your ears so that you may at least hear me when I speak.

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

What are words for 'gamble(noun and verb)' and 'gambling'? "The sailors had taken many gambles with the sea I took a gamble that stock prices ....

"What are words for 'gamble(noun and verb)' and 'gambling'? "The
sailors had taken many gambles with the sea I took a gamble that stock prices
would rise." or "I took a gamble that stock prices would rise." or " and "The most
characteristic form of English gambling is betting through a bookmaker." and "He
gambled his reputation on the outcome." What are words for 'hustle(noun and
verb)'?" "The guy tried to hustle me into buying into a bogus real estate deal."
or "The guards hustled the prisoners into the jail." and "He finally got wise to
his hustle and threatened to call the police." or "Steve showed a lot of good
hustle today in practice." 

to gamble → pran chans, pran ris (pran risk), parye, fè paryaj
a gamble→ chans, ris (risk), aza, paryaj
to hustle → bouskile, pouse,  bourade
hustling → sakaj, tapaj, aktivite, bourad

1.  Anpil Ayisyen te pran chans ak lavi yo lè yo te pran kanntè pou vin Etazini.
     A lot Haitians took a gamble on their lives when they got on a boat to come to the US.

2. She's paying a gambling debt.
    L'ap peye yon dèt li te fè nan paryaj.

3. We hustled our way to the front of the stage.
     Nou te bourade moun pou n rive devan podyòm nan.

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

cynical, sarcastic, sarcasm, ironic, irony

to be sarcastic → ridikilize, pase nan betiz, fè mokri
sarcastic (cynical, ironic) → ridikil, ap fè mòkri, sou mòk
sarcasm  → ridikilizasyon, derizon, mòkri
irony → derizon

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

Eske 'we pa we' vle di menm bagay kom 'kout ke kout'?

Yes, basically.

wè pa wè (whether ou show up or not, whether you're here or not, ready or not)
1. Wè pa wè, antèman an pou katrè (expression)
    Ready or not the funeral is for four o'clock.
    meaning: Death waits for no one.

vle pa vle (like it or not)
2. Vle pa vle, fò w demenaje kay la nan twa jou.
    Like it or not, you must move out in three days.

kout ke kout (no matter what)
3. N'ap suiv Jezi kout ke kout.
    We'll follow Jesus no matter what.

bout pou bout (little by little, eventually)
4. Bout pou bout, n'a rive.
    Little by little, we'll make it.

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

Eske ou tradwi fraz sa a pou mwen: "Li t ap souke nan van ki t ap vante a cheve l kite koulè lò"? Mesi

Li         []  t ap souke    [] nan van    [] ki t ap vante          []  a
He/she [] was shaking  []  in wind    [] that was blowing   [] the

cheve  []  l            [] ki te koulè        []  lò
hair     [] his/her    [] that was color  [] gold

She was waving her golden hair in the wind that was blowing
Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

Kisa vle di 'fe twalet' egzakteman?

fè twalèt → to take a bath, to clean up, to wash up, to take care of your hygiene
fè twalèt can also mean to wash up your private parts, especially when Haitians say fè twalèt deba (which applies mostly to women).
Fè twalèt deba (for many since there's no running water) will consist of sitting on chamber pot that is filled with water and ... you know... take good care of the V. 

Examples:
See how we use it like a pronominal verb with the pronouns after it (underlined).

1. Al fè twalèt ou.
    It's like saying: Go wash yourself up.  or Go do your wash (lit.)   
    Go wash up.

2. Mwen poko fè twalèt mwen.
    I haven't washed up yet.

3.  Kilè li te gen tan fè twalèt li?
     When did she have the time to wash up?

4. Al fè twalèt de ba w.
    The same goes here with the pronouns.  They will follow "deba".
    Go wash up.

5.  Chak maten manman tifi a fè'l al fè twalèt deba l nan larivyè a.
      Every morning the girl's mother have her wash up in the river.
    
Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

Ki sa ki tout siyifikasyon pou mo 'nève' a?

nève (or enève) (intransitive) → to become very angry, to be mad, to be upset
nève (or enève) (transitive) → to irritate s.o,  piss off

1. Misye te nève, donk li ba chen an yon kout pye.
    He was mad, so kicked the dog.

2. Gen moun ki p'ap travay ki resevwa bon asirans lasante.  Mwen menm, m'ap travay di e m pa menm gen mwayen pou al kay dantis chak ane.  Sa nève'm.
     There are some people who aren't working who receives good health insurance.  I'm working very hard and can't even afford a yearly dental visit.  This pisses me off.

Also, nève can also be use to translate nervous (as in nervous system)
3.  Maladi a te atake system nève li.
     Maladi te atake tout nè li.
     The disease attacked his nervous system.

and of course, we have the word neve (without the accent on the first "e") which is Creole for nephew.
Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

What's the Haitian Creole word for 'to give up'? "He was surrounded, so he gavehimself up." or "They gave up the search when it got dark." or "He gave up his seat to an old man." or "I gave up my faith years ago." or "OK, I give up, you

There are many ways you can say "to give up" in H. Creole.
to give up → sede, abandone, bay legen, bat ba, kite sa, lese tonbe

1. He was surrounded, so he gave himself up.
    Yo te sènen li donk li bay legen.
    bay legen, bat ba → to cede, to surrender, to yield

2. to give up something
     abandone bagay la
     kite bagay la tonbe

3. Give it up.
     Kite sa.
     Lese l tonbe.

4. He gave up his faith years ago.
    This one seems to say that he's abandoned his faith years ago.
    Li abandone relijyon li kèk ane pase.

5.  I give up. You win.
     more like .....I surrender
     M bay legen.  Se ou k genyen.

6.  He gave up his seat for an old man. 
     Li abandone plas li pou yon mesye pèsonaj.
     Li kite plas li bay yon mesye pèsonaj.
     Li sede plas li bay yon mesye pèsonaj.

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

How would you say "I didn't like the car." Also what are the contraction and long forms for negatives? Ex: pa't = pa te. Thanks

I didn't like the car.
Mwen pa te renmen machin nan.
Mwen pa't renmen machin nan.

negatives: long form and contraction
past tense
Mwen pa't konnen. (contraction)
Mwen pa te konnen. (long form)
I didn't know.

Future
Mwen p'ap kapab ale. (contraction)
Mwen p'ape kapab ale. (contraction)
Mwen pa ap kapab ale. (long form)
I will not be able to go

Progressives
Mwen p'ap etidye kounye a. (contraction)
Mwen pa ap etidye kounye a. (long form)
I'm not studying now.

Mwen pa t'ap dòmi lè w te rantre yèswa. (contraction)
Mwen pa te ap dòmi lè w te rantre yèswa. (long form)
I was not sleeping when came in last night.

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

In one of your previous posts, I learned a new expression 'ti tak'. .....

In one of your previous posts, I learned a new expression 'ti tak'.
It pushed me to make a list of other expressions that express the same
meaning,which I have collected: ti kal, ti zing, ti gout, ti moso, ti kras, ti
bab, ti chikèt, ti(yon) filèt, ti lougal, ti (yon)kwendak, ti pwèlyèm, ti yota,
ti yik, ti tak. I know that haitian creole is a rich language; so, are there
other expressions of small quantity that exist that is not on that list? I feel
like there are more; I hope there are more.

Of course, there's always more in Creole :)
I wish I knew them all.  The more you travel to different regions of the country, the more you'll learn.
I'll add a few to your list:
ti lòsyè
ti kraze
ti krabinay
ti zuit
minizuit
miniminizuit
I think they also say piti piti zuit

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

What are words for 'somewhat' or 'slightly'? "He felt somewhat .....

"What are words for 'somewhat' or 'slightly'? "He felt somewhat
awkward in his suit." or "Our work has progressed somewhat." or "The course is
somewhat more difficult than I was told it would be."  or "He weighed slightly
less than his wife who was a foot shorter."

somewhat → yon ti jan
slightly → yon ti jan, enpe, yon ti kras, lejèman

1. "He felt somewhat awkward in his suit."
    "Li te yon ti jan malalèz nan kostim li an."

2. "He weighed slightly less than his wife who was a foot shorter."
    "Li te peze lejèman mwens pase madanm ni ki te kèk pous pi kout pase l."


Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

What are words for 'to lead to'? "Drug use often leads to crime." or "Poor eating habits may lead to health problems." or "Continued hatred of a certain group of people will one day lead to genocide."

to lead to → koze, lakòz

"Poor eating habits may lead to health problems."
"Move rejim alimantè kapab koze pwoblèm lasante."

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

What are some words for 'bane' and 'boon' respectively?

"What are some words for 'bane' and 'boon' respectively? "The bane of
my existence."  or "Fighting this war in the Middle East is a bane to the
American economy." and "Finding the dry cave was a boon to the weary travelers."
or "Anesthetics are a great boon to modern surgery."

bane → lamizè, kalamite, bosko, devenn
boon → benediksyon, avantaj, bone, koutchans


Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

What are words for 'woods'? "I was lost in the woods."

woods → bwa, raje

I was lost in the woods.
Mwen te pèdi nan raje a.

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words

How does one translate "what does the subject on abortion has got to do with writing about black slaves?" Emphasis on "got to do". What are ways to say it?

has to do with → gen pou wè ak, ki relasyon ki gen ant, ki koneksyon ki gen ant

1. What does one has to do with the other?
     Kisa youn gen pou wè ak lòt la?

2. "What does the subject on abortion has got to do with writing about black slaves?"
     Kisa ekri sou esklav nwa yo gen pou wè ak koze avòtman an? 
     Ki koneksyon ki gen ant ekri sou esklav nwa yo ak koze avòtman an?
Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words