Stupid question about sharing wifi?

With the right tools and right techniques, yes he can. But it's not like he can open his web browser and just watch what you're doing.....it's far more involved than that and he will have to intentionally go out of his way to do so.

I wouldn't recommend doing anything sensitive like managing your bank account.

Yes he can. Use a VPN with encryption. There should be a couple free versions out there on the web. I use a paid VPN service.

If your neighbor knows about networking and is very technically savvy, then yes he could see what you're doing online.

If he was computer savvy he could look at the routers logs and find out what sites you have visited.

Yes he can.

If he is smart then off-coure he can.