Thank you and Ke Bondye beni ou ak fanmi ou! Do 'fòk' and 'dwe' have the same meaning?

Yes, they both express necessity.  The only difference is that fòk comes before the subject, and dwe comes after the subject in a typical sentence.

Examples:
I must go.
Mwen dwe ale.
Fòk mwen ale.


You must speak to her.
Ou dwe pale avè li.
Fòk ou pale avè li.

Also, there are many other synonymous expressions such as fòk and dwe that express necessity or obligation in Haitian Creole.

You may say fòk, or fò, dwe, fèt pou, sipoze, oblije or blije.
Just remember that fòk or fò must come before the subject
Also, you can have a contraction after ''fò", but not after "fòk", as you can see in the following examples.
Contractions follow vowels (nasal and non-nasal), not consonants.

Examples:
Fò'w mache anvan ou kouri.
You must walk before you run.


Fò'w pa kwè tout sa yo di'w.
You should not believe everything they tell you.


Fòk ou pa kite'l fè sa.
You must not let him do that.


Yo sipoze ban nou mwatye nan lajan an.
They should give us half of the money.


Ou oblije prezan nan maryaj pitit fi ou.
You have to be present at your daughter's wedding.


Ou sipoze mete pantalon'w anvan ou mete soulye'w.
You must put on your pants before you put on your shoes.


Ou fèt pou bwose dan'w chak swa anvan'w monte kabann.
You must brush your teeth every night before you go to bed.


See these helpful links:  Origin of the word Fòk in Creole, Fòk and Fò

Fòk gen maladi pou gen lanmò.?

I would have to disagree with this proverb.
It is not true in life at all.
If it's not true in life, what purpose does it serve as a proverb?
Sickness does not always precede death.

Is there any real difference between "fòk ou...", "ou dwe...", "ou fèt pou...", and "piga ou...", other than the last one is negative?

No, not much difference.
They're all about obligation, necessity, duty.

Pinga ou is also about giving a warning or advice.

Examples:

You must go talk to her. (can be accurately translated many ways in Creole)

Fòk ou al pale avè l.

Fò w al pale avè l.

Ou dwe al pale avè l.

Se pou w al pale avè l.

Ou fèt pou w al pale avè l.

Ou oblije al pale avè l.

Pinga ou pale ak moun ou pa konnen.

Don't talk to strangers.

Pinga w al dòmi san priye.

Don't go to bed without praying.

Pinga ou bliye m.

Don't you forget me.

Pinga ou ouvè bwat sa a.

Do not open this box.

Ask me anything

fok ou pale ak mwen demen matin bon nuit (in English please)

Fòk ou pale ak mwen demen maten. Bòn nwi.

You must talk to me tomorrow morning. Good night.

Ask me anything

What is the origin of the Haitian Creole word FOK?

Fòk - comes from the French: 'FAUT QUE' as in 'IL FAUT QUE'.

Fòk or Fò (v.) → must, have to

When using the verbs Fòk or Fò in a sentence, the subject will come after the verb.

Please notice how I place the subjects or subject pronouns after the verbs Fòk and Fò.

Examples:

1. Fòk mwen ale.

    I must go.

2. Fò m pale avè w

    I must talk to you.

3. Fò ou vini wè mwen.

    You must come to see me.

4. Fòk nou goumen pou libète nou.

    We must fight for our freedom.

5. Fòk bagay yo chanje.

   Things must change.

6.  Pa rete nan kabann.  Fòk ou leve.

     Don't stay in bed.  You have to get up.

negative sentences with Fòk and Fò

7.  Fò w pa pale konsa.

     You must not talk like that.

8.  Fò w pa al dòmi ta, tande!

     You must not go to sleep late, you hear!

9.  Fòk ou pa aji konsa!

    You must not act like that!

Fòk sa chanje!

Yes, i agree with you. And everyone agrees with you, too, that 'things must change'. Would you mind taking the first step :)

Ask me anything