Learn Polish: Kiedy on gotuje byle jak, jemy byle co. - When he cooks carelessly, we eat just anything.

Literally, yes, but it usually carries a negative connotation. It means doing something carelessly, sloppily, or without effort. So gotuje byle jak means he cooks without caring about the result.

What is the difference between byle co and cokolwiek here?

Byle co implies indifference to quality, often meaning 'just any old thing,' 'whatever is lying around,' or even 'junk.' If you used cokolwiek, it would sound more neutral, simply meaning 'anything at all'.

Are byle jak and byle co always written as separate words?

Yes, when byle is used as a particle with a pronoun or adverb like co, kto, or jak, it is written separately. However, watch out for the related adjective bylejaki (meaning mediocre or shoddy), which is written as one word.

Is it necessary to add a word like wtedy (then) before jemy?

No. Just like in English where you can say 'When he cooks, we eat,' Polish connects the two clauses perfectly well with just a comma. Adding wtedy is grammatically fine but unnecessary.