How does one translate the Future Perfect? Examples, "By next November, I will have received my promotion.", "By the time he gets home, she is going to have cleaned the entire house.", "I will have been in London for six months by the time I leave."

Much like the future tense.

1. "By next November, I will have received my promotion."
     "Lè novanm rive, m'a gentan resevwa pwomosyon mwen."

2. "By the time the guests arrive, she will have cleaned the entire house."
    "Ditans pou vizitè yo rive, l'ava netwaye tout kay la."

3. "I will have been in London for six months by the time I leave."
    "M'ava gen si mwa nan vil Lond anvan mwen kite."

4. By the time I return to Haiti, you will have forgotten me.
    Distans pou m tounen Ayiti, w'a bliye m.

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How does one translate the Present Perfect Progressive? Examples, "She has been working at that company for three years.", "She has been watching too much television lately.", and "Lisa has not been practicing her English."

Much like the present continuous form:

1.  "She has been working at that company for three years."
     "L'ap travay nan konpani sa a depi twazan."

2. "I notice that she has been watching too much  television lately."
     "Mwen remake ke l'ap gade twòp televizyon tou dènyeman." 

3. "Lisa has not been practicing her English."
     "Lisa pa ap pratike Angle li."

4. I have been trying to help you all these times.  But it seems that you don't understand that.
    Se eseye m'ap eseye ede w tout tan sa a.  Men sanble ou pa konprann sa.

5. I've been living in this neighborhood for twenty years.  I've never seen anything like this.
    M'ap viv nan katye sa a pou ventan.  Mwen pa janm wè yon bagay parèy.

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How does one translate the Present Perfect? Example, "The government has become more interested in arts education." Another example, "I have been to France." Last example, "I have seen that movie six times in the last month."

Pretty much like Haitian Creole's past tense (using the paste tense indicator "te").  Don't be surprised if natives omit that "te" sometimes.

1. "The government has become more interested in arts education."
    "Gouvènman an te vin pi enterese nan edikasyon travay atistik"

2. "I have been to France."
     "M te vizite peyi Lafrans." 
     "M te vwayaje an Frans"
     "Mwen te fè ti pase an Frans."
       or
      "Mwen t'ale nan peyi Lafrans."

3. I have not received your letter yet.
    Mwen poko resevwa lèt ou a.

4. "I have seen that movie six times in the last month."
     "Nan mwa pase a, m te wè fim sa a sis fwa."

5. I have seen what hatred can do. And it's not a beautiful thing at all.
    Mwen wè sa rayisman ka fè.  E se pa yon bagay ki bèl ditou.

6.  Have you lost your mind?! 
     Eske ou pèdi tèt ou?!

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How does one translate the Past Perfect Progressive? Example, "Betty failed the final test because she had not been attending class." Another example, "Jason was tired because he had been jogging."

Use the combination te (past tense indicator) + ap (progressive form indicator)

1.  Betty failed the final test because she had not been attending class.
     Betty te echwe nan dènye egzamen an paske li pa t'ap prale nan klas.

2. "Jason was tired because he had been jogging." 
      Jason te fatige paske li te ap kouri.
     Jason te fatige paske li t'ap kouri.

3. She had been talking to her friends when she collapsed.
     Li te ap pale ak zanmi l yo lè li te pèdi konesans.
    Li t'ap pale ak zanmi l yo lè li te pèdi konesans.

4.  If you had not been crying, they would have never found us.
     Si ou pa t'ap kriye, yo pa ta janm jwenn nou.

5.  If you had been watching the baby instead of talking on the phone, all this would not have happened.
     Si ou t'ap veye bebe a angiz ap pale nan telefòn, tout sa pa ta janm rive.

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How does one translate the Past Perfect? Is it with Te or not? Are there are ways of expressing this tense? Example, "She only understood the movie because she had read the book." Another example, "We had had that car for ten years before it broke down."

Past perfect is expressed with "te"

1.  "She only understood the movie because she had read the book."
     "Li te konpran fim nan senpleman paske li te li liv la."

2. "We had had that car for ten years before it broke down."
    "Nou te gen machin sa a pou dizan anvan l te vin pran pàn."

3. If you had not been there, I don't know what I would have done.
    Si ou pa te la, m pa konn sa m ta fè.

4. I had waited for about two hours when she finally decided to show up.
    Mwen te tann pou dezèdtan konsa lè li te resi deside pou l parèt.

5.  We had never seen anything like this.
      Nou pa't janm wè yon bagay konsa.

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what does ki es ki te di ou sa? mean

I think you mean:
Kiyès ki te di ou sa?
or
Kilès ki te di ou sa?
or
Kimoun ki te di ou sa?
Who told you that?

Lòt egzanp:
Kilès ki te rakonte w istwa sa a?
Kiyès ki te envite w?
Kilès ki te di w pou w vin la a?

Kimoun ki di w ou te toutouni?

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Yuca (root vegetable?) in Creole

yuca is manyòk in Creole

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I go to church this morning

Do you mean "I went to church this morning" → M t'al legliz maten an.

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Ou fache avè m?

Did he/she pick a bad vibe?

Ou fache avè m?
You mad at me?

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Regarding Translating "let's move forward" or "we re moving forward", I can see why I'll see many different variations for just one little sentence

yeah, I guess you found out that each Creole word that translates these sentences may have their own variants

Let's move forward
An'n vanse douvan
An'n vanse pou pi devan
and more...

We're moving forward
N'ap vanse douvan
Nou pral vanse pou pi devan
N'ap vanse pou pi devan
and more...

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i am moving forward for the new year. i can not control the situation so i am letting it go

Moving forward → fè devan, fè douvan, vanse devan, vanse douvan, vanse pou pi devan, ale pi devan, ale pi douvan

I am moving forward for the new year. I cannot control the situation so i am letting it go 
M'ap vanse douvan pou ane nouvèl la.  M pa ka kontwoke sitiyasyon an, donk m'ap kite'l tonbe

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

"genyen rekonesans" nan Angle?

Genyen rekonesans → to be grateful towards

1.  Mwen genyen w rekonesans.
     I am grateful towards you. (is it towards?)

2. Nou genyen tout fanmi ou rekonesans pou sa w fè pou nou.
    We are grateful towards your whole family for what you've done for us.

3.  Nou dwe gen paran nou rekonesans pou bon levasyon yo te ban nou.
     You must be grateful towards your parents for our exceptional upbringing.

4. Si se pa't manm legliz yo, mwen pa t'ap la a.  Se pousa mwen genyen yo anpil rekonesans.
    If it weren't for the members of the church I wouldn't be here.  That's why I am very grateful towards them.

5.  Jezi ban nou lavi, men nou pa genyen l rekonesans.
     Jesus gave us life, but you are not grateful towards him.

6. Pou sa m fè pou ou, pou w pa genyen m rekonesans.
    For all that I've done for you, and you don't show me any gratitude.

7.  Timoun, alèkile, pa gen paran yo rekonesans.
     Kids, these days, don't show their parents any gratitude.

8. Ala ou rekonesan!
    How grateful you are!
    
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finishing a letter, "Love, Cindy"?

Love, Cindy
Avèk lanmou, Cindy

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I like this in Sixto's Zabèl: "Gen priyè pou chase move lespri, men pa gen priye pou chase vakabon. Men vakabon, se an vakabon ou aji avè'l pou w regle ak li".. To be sure about the last part, is it saying you have to stoop to someone's level...?

Yes. basically.  "vakabon", here, translates a villain, scoundrel, or someone with whom you can't play "nice".
examples
Vòlè, se an vòlè ou aji ak sa pou'w regle ak yo.
Avadra, se an avadra ou aji ak sa pou'w regle ak yo.
Pye sal, se an pye sal ou aji ak sa pou'w regle ak yo.
Bandi, se an bandi ou aji ak sa pou w regle ak li.
You must stoop down to their level in order to deal with them.

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

SEXY LADY

O O!  Se sa menm wi!

HAITIAN STYLE
Se pa tann dat Ayisyen ap fè Gangnanm Style :)
BY SWEETCOCONUTS

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