Merhaba.

In both of these examples:

* Bileti olan kimse var mı?

* Biletleri olmayan kimse sinemaya gitmiyor.

is it possible to remove kimse with no other changes (only adding punctuation) and the sentences will still be correct?

Yes, it is perfectly ok to remove those "kimse" from the sentences above and still make sense. In fact, it makes more sense without "kimse". Since "kimse" does not suit on those sentences. 

In the second sentence, do you mean " The ones who don´t have ticket can not go to the cinema ? " , if so, then you should say "gidemez". And plus "Bilet" should be singular.

" Bileti olmayan sinemaya gidemez. "

Oh, yeah, you´re right. I didn´t mean to put "ler" there, I just rewrote this example from a sentence which looked a bit differently and I forgot to remove it.

But still I have a additional question

Don´t you think that if we write the sentence like this: 

" Bileti olmayan sinemaya gidemez. "

it is becoming a little ambiguous?

It can be understood as "(He/she) doesn´t go to the cinema which  has no ticket".. It is like the "olmayan" part was an adjective describing cinema, isn´t it?

It is not ambiguous at all.  

Bileti olmayan [kişiler] sinemaya gidemez.

The adjective there is  hidden in the sentence which is " kişi[ler] "  so, the adjective is "kişi[ler]" --> person [people]

People who has no ticket ---> People is described here. 

Ok, I will give another example of this kind.

Yesterday I saw this in Turkish press: Bu kadını tanıyan polisi arasın.

I think it´s supposed to mean Let the one who knows this woman call police. (= Call police if you know this woman). But that understanding wasn´t so obvious at first and I had to read the sentence three times to get the right sense.

So now it is my question- how would you say "Let her (or him) search for the policeman who knows this woman!"... isn´t it also Bu kadını tanıyan polisi arasın! ??

Interesting views, sufler.

Not that I know but it looks like Turks have the tendency of looking for the subject at the beginning of the sentence. And only if there is no constituent suitable for this purpose other interpretations (like dropped 3rd person pronoun) pop up.

Just a comma removes the ambiguity.

bileti olmayan (the one who has no ticket)

Bileti olmayan sinemaya gidemez. | For the learners, this may create ambiguity as "bileti olmayan sinema (the cinema that has no ticket)".

But, if we put a comma after the subject:

Bileti olmayan, sinemaya gidemez. (Who has no ticket isn´t allowed to go to the cinema.)

bu kadını tanıyan (the one who knows this woman)

Bu kadını tanıyan polisi arasın. | The learners may perceive the subject as if it is "bu kadını tanıyan polis (the policeman who knows this woman)". It requires to put a comma after the subject:

Bu kadını tanıyan, polisi arasın. (Let one who knows this woman call the policeman.)