Learn Polish: Czyj jest ten komputer? - Whose is this computer?

Czyj means 'whose', and like adjectives in Polish, it changes its ending to match the gender of the noun it belongs to. Since komputer is a masculine noun, we use the masculine form czyj. If we were asking about a feminine noun like książka (book), we would use czyja.

I usually say to jest for 'this is'. Why does this sentence use ten instead of to?

When you are just pointing out what something is (like 'This is a computer'), you use the fixed phrase to jest. But here, you are talking about one specific computer: 'this computer'. When 'this' is attached directly to a noun to describe it, it must match the noun's gender. Ten is the masculine word for 'this' to match the masculine noun komputer.

The lesson is about the Genitive case for possession. Are any words in this sentence in the Genitive case?

Actually, no! Every word in this sentence is in the basic Nominative case (the dictionary form). However, this question asks about possession. The answer to this question is where you will use the Genitive case. For example, if you answer 'It is Adam's computer', you would say 'To jest komputer Adama', where Adama is in the Genitive case to show ownership.

Can I change the word order and say Czyj to jest komputer?