Ok, so if both sentences are correct what's the difference

He will work on Tuesday or He is working on Tuesday.

For example It's Monday and I want to ask somebody whether he/ she works tomorrow, what should i say:

Are you working tomorrow ( I believe it's correct because it refers to arrangements)

Will you work tomorrow?

Is it true that if we don't know how many hours we will work or with whom we should say I will work tomorrow or ask who will I work tomorrow with

or for example it's Tuesday we have just come and want to ask our supervisor, who are we working today with or who will we work today with?
He will work on Tuesday = A future fact based on present knowledge.

He is working on Tuesday = An arrangement for the near future

For example It's Monday and I want to ask somebody whether he/ she works tomorrow, what should i say:

Are you working tomorrow ( I believe it's correct because it refers to arrangements-- Yes.)

Will you work tomorrow?-- A little odd, since it does not state a fact, but possible.

Also: Are you going to work tomorrow? Do you work tomorrow?

Is it true that if we don't know how many hours we will work or with whom we should say I will work tomorrow or ask who will I work tomorrow with-- No, not true at all.

or for example it's Tuesday we have just come and want to ask our supervisor, who are we working with today or who will we work with today?-- Both of these are OK, too, or the other options I gave above.

Do you work tomorrow?
I didn't know it is possible to use Present Simple in that way(I'm surprised)...

Is it possible to use Present Simple to express future in questions only, or it would be also correct to write:

I work tomorrow.
Site Hint: Check out our list of pronunciation videos.
I work tomorrow is also fine, as is I don't work tomorrow, so we can see a movie together.
Present simple can express scheduled future actions.

Ex. The movie starts at 10.

Ex. Tomorrow is sunday.

Ex. I have English class tomorrow.

Regards.