I also find the ics browser better than chrome beta and others. As far as the keyboard try SwiftKey I prefer that over stock. Once chrome comes out of beta hopefully soon it should run better but for me it's still to buggy at the moment on the prime.
I am partial to the Opera browser. I like keeping the title bar visible at all times, and it just seems a little faster than the stock browser. Also, it seems to get hung up less than the stock browser on website, like Amazon.com being an example.
I Thought the same of the built-in as well until I got used to it. Occasionally I'll use Chrome just to deviate and not get "too settled in". I always seem to go back to the default. As far as the keyboard issue you speak of, remember that the screen is a capacitive device. Where your fingers (both) are at any given time can effect it. I've found myself with my "holding" hand sometimes too close to the screen, effecting the outcome of tapping. For lots of typing I use the docking station.