1. Yes. I visit Amiga.org with my A1240PPC and AWeb 3.5 beta and everything is cool and reasonably fast, thanks to PPC datatypes. I often check it too with my A630 and mere ECS on my A1085 640*256 screen with AWeb 3.4, and it is still readable though heavy scrolling is required. Currently though, i am browsing on my PC laptop which i have to admit is far superior to any of my amigas.
2. 68030 is ok with some good datatypes and a good browser. Maybe, IBrowse would be the faster choice for you rather than AWeb. Try them both. WiFi runs brilliantly on A600/A1200 PCMCIA.
3. Yes, it is way cooler than a 1240.