Let me try to answer some of your questions (numbering corresponds to your numbering):
1. Can't beat push email with a BlackBerry. Email is where it shines. You shouldn't have any problems. You can set up to 10 email accounts and have the emails pushed to your phone.
2. I'm not too familiar with OTA sync with Google as I don't use it, but as for Outlook, you can definitely sync your calendar, contacts, notes, tasks with the BB. That's what most people use.
4. I think Opera Mini for BlackBerries is a pretty standard software. Again you shouldn't have problems with it. BBs also come with their own browsers -- which I've found to be a bit better than Opera Mini for some things.
5. I use AvantGo on my BB, but I dont have a data plan. Worse come to worse if the software install doesn't work for you, you can just use it like you are visiting the website.
7. Google Maps work on BBs. There's also a BlackBerry Maps program built into the phones. Some debate about which is better.
8. Yes you can play videos. Dont think avi format works. I use the BlackBerry Desktop media manager to transfer my videos over to the phone and it converts it to mp4 format I believe.