Translation:My lawyer does not work with the police.
"Współpracuje z policją" perhaps sounds just a bit better, but the word "współpracować" in some aspects has a broader meaning (it means voluntary and productive cooperation) than just "pracować", so it is not the same, particularly in a phrase with negation.
If you say "Mój prawnik nie współpracuje z policją" , the first meaning of this phrase is that he may be doing something with the police - because he is forced to - but he does his best to sabotage the advancement of investigation or to block the prosecution.
In the contrary, the phrase "Mój prawnik nie pracuje z policją" means that he plainly refuses to cooperate with the police.
Yes. Please see: https://www.clozemaster.com/blog/polish-prepositions/