Is there a way to distinguish b/t there are/there will be? I have/I will have?

Yes.

Present tense:
there is/ are - genyen, gen

(gen or genyen are used interchangeably)

examples:

There is a house here. - Gen yon kay la.

There's a woman in the car. - Genyen yon fanm nan machin nan.

There are many cars on the road. - Genyen anpil machin la dou wout la.

Future tense:
For the future tense, use either ap or pral.
there will be - pral genyen, pral gen   or  ap gen, ap genyen
examples
There will be many people here.
Pral gen anpil moun la.

There will be dancing.
Pral gen danse.

There will be a lot food at the party.
Ap genyen anpil manje nan fèt la.


The same form goes for Past Tense:
Use the paste tense determiner te
examples
There was a man here.
Te gen yon mesye la.

There were many people at the party.
Te gen anpil moun nan fèt la.

There was a book on the the table.
Te gen yon liv sou tab la.

Same goes when using would, should, could

would - ta
could - ka
should - ta dwe

example:
There would have been a fight if I wasn't there.
Ta gen yon batay si m pa te la.

There should be enough food for everyone.
Ta dwe gen ase manje pou tout moun

There may be another dog in the backyard.
Ka gen yon lò chyen nan lakou a.

And if you need to put these sentences into the negative form,
place 'pa' in front of the sentence.  'pa' is the determiner for the negative form.
examples:
Another way to say there's no, there are no..., there's nothing (in the present tense) is NANPWEN

Pa gen pèsonn / Pa gen moun
Nanpwen pèsonn / Nanpwen moun  
There's no one

Pa gen lekòl jodi a.
or
Nanpwen lekòl jodi a
There's no school today.

Pa gen manje nan kay la.
or
Nanpwen manje nan kay la.
There's no food in the house


Pa gen anyen la.
or
Nanpwen anyen la.
There's nothing here.

Pa gen pèsonn mwen renmen plis pase w
Nanpwen pèsonn mwen renmen plis pase w.
There's no one I like better than you.

Pa pral gen batay. (un-contracted)

P'ap gen batay. (contracted)

There will not be any fight.

Pa te gen yon kamera la. (un-contracted)

Pa't gen yon kamera la. (contracted)

There was not a camera there.

Pa ta dwe gen ti moun nan fèt sa.

There should not be any kids at this party.

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