Ok, thanks for your answers.

How about this sentence.

We are talking to friends and one of our friend's is asking y friend about table tennis next week.

I would like to say that he is working on Tuesday but I don't know when he finishes/ will finish?

Thanks in advance
1 2
He is working on Tuesday, but I don't know when he finishes/ will finish.

Both are OK, but native speakers usually use present for future in such dependent clauses. Notice that you used a present verb form for future in your first clause also.
Mister Micawber He is working on Tuesday, but I don't know when he finishes/will finish.
I'm curious to understand why you have used continious(... is working ...)

In my opinion, it should be correct to write:

He works/will work on Tuesday, but I don't know when he finishes/will finish
I suppose that as the sentence is compound we have two independent sentences:

1. He works/will work on Tuesday (So that I would never use is working in that context as there is no continious action)

2. I don't know when he finishes/will finish
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Well, in fact I used continuous because layla did, but nevertheless, it is a perfectly fine future verb form and works well in layla's sentence. Present continuous is commonly used for arrangements in the near future. It has nothing to do with continuous action.

Your #1 and #2 are also acceptable forms.
Thank you for your answer
As I understood the Present Continious as well as the Present Simple can be used to express smth. in the future in Simple sentences.

The Present simple is usually used to inform about future movement processes(to leave, to start, to come, to return)

He arrives London on Monday

We return home tomorrow
The Present Continious is used to express that smth. will definetly happen or that somebody is going to do something

I'm going to win this competition next year

She's leaving tomorrow

They are buying a new car soon
Am I right?
 
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Well, your 3rd example ('I'm going to win') is a third, different future form, and using other future forms in your definition for the present continous ('will happen', 'is going to do') also clouds the issue. I don't think that present simple is particularly connected with 'movement processes', since the same verbs appear in continuous as well. Here are some quick, rough definitions for these four future forms:

He arrives in London on Monday. = a sure schedule

He's arriving in London on Monday. = a near-future arrangement

He's going to arrive in London on Monday. = that his his plan.

He'll arrive in London on Monday. = a future fact based on present knowledge.

However, meaning and situations often overlap, so that native speakers may use one or another unconcernedly.
I thought that present simple is connected with 'movement processes' as it isn't used in other cases to express the future(but I'm not sure).

They will buy a new car soon - correct

They are buying a new car soon - sounds good

They buy a new car soon - seems to be mistaken

The steamer sails tomorrow - should be correct

The steamer is sailing tomorrow - I suppose this sentence to be correct too

He is taking his examination on Monday - correct

He takes his examination on Monday - It is not correct(in my opinion)
Could you clarify the aspects of the usage of Present Simple in that context?

Thanks in advance
I have never heard of 'movement processes', nor do I know what you mean by that. Perhaps you can explain in light of these two sentences:

They buy a new car soon -- This sounds odd.

He takes his examination on Monday -- This is good.
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