Some services? I have not found any Google service to work over there. Which one should work?

Gmail works, in the sense that Shanghai utility is able to deliver e-mails to me when it's time to pay the electricity bill. Downloading stuff from google's android repostitories (i.e. for developing Android) also works (most of the time).

Yes the latter works (Android repos which are not on google.com), but when in Shanghai I get nothing from Gmail, ever. Not sure how that works then but at least it's not supposed to work I guess as that's officially banned. And when something works from Google it'll not work after trying it a few times. I definitely find it both hard to work there and both relaxing. Hope to be in Shanghai soon again.

Comply with what? What law is being broken here?

Censorship laws, mainly. China wants to block out huge portions of search results, and Google doesn't want to do that.