Mine has a bug in the last OTA meaning it reboots at random (it's even present in custom ROMs too). It normally reboots once every 2 days or something, sometimes more frequently. It's been fixed in 4.3, but I've not had time to flash a 4.3 ROM.
Because of that, I can't remember the last time I intentionally rebooted. It's fairly infrequently though.
Sorta the same. "If" I use it as an alarm then it needs to be left on and will stay on until I don't need it as an alarm when I'll turn it off when I go to bed. So, it could be on for 16 hours, or it could be on for a couple of weeks.
When I rooted my phone, I had to restart it weekly as the performance degrades over the course of a week. Before I rooted it and after I unrooted it, I only reboot once a month. Normally, if I noticed something is not behaving properly, that is one of the things I do. More often than not, it was some other issue.
This past month, I had to reboot a few times due to the new 4.3 update on my SGS3. I had a few issues and was trying to reboot it to fix them. It turned out I just had to reinstall some apps and that's it. It has been a few weeks since I've rebooted my phone now.