What is the widest tire I can fit on my 32c wheels?
Assuming that your rims are actually 622x15 ISO size, like the Shimano page for those rims says...

According to this handy chart on Sheldon Brown's site, putting a 35mm tire on a 15mm rim is slightly bigger than recommended. It's close enough that it should be fine, however. That chart is fairly conservative (and even says so at the bottom).

As far as the widest, you could put 42mm on there if the fork, brakes, stays, bridges and seat tube all have the clearance, but that's really pushing it quite far and likely to cause poor handling or other issues. 35mm is just barely pushing it and should be fine.