[General] Crossword and chess

[Silverobama]

Context 1:

I have a friend who loves crossword games. Today I met him and asked "Feel like playing a crossword?" Is it natural to ask this question?

Context 2:

I also have a friend who can play chess well. If I want to play with him, is it natural to ask him "Do you want to play a chess with me"?

 

[GoesStation]

We don't play a crossword puzzle, we solve it or do it, so number one doesn't work. Number two is fine.

Are crossword puzzles possible in Chinese?

 

[emsr2d2]

Context 1:

I have a friend who loves crosswords. [STRIKE]games.[/STRIKE] Today I met him and asked "Feel like [STRIKE]playing[/STRIKE] doing/solving a crossword with me?" Is it natural to ask this question?

Context 2:

I also have a friend who can play chess well. If I want to play with him, is it natural to ask him "Do you want to play [STRIKE]a[/STRIKE] no article here chess with me"?

See above. We don't call a crossword a game. It's just a crossword or a crossword puzzle. As GS said, we don't use "play" with crosswords. I added "with me" because without it, you're just asking him if he feels like doing a crossword, which is usually a solitary activity.
If you want to use the indefinite article in the second context, you'd have to say "... a game of chess". It's never "a chess".

 

[Silverobama]

Are crossword puzzles possible in Chinese?

Yes.