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