Add to Problem 2: after online, premiere won't play until reboot.
Problem 1: For all sequences? Just existing sequences? Have you tried creating new ones?
Problem 2: What's 'going online' mean here? Are you starting up a browser? Are you on a dial-up connection, or always-on broadband?
Problem 1: sound cut out on track one seems to be random, corrected temporarily by changing sequences, tracks. But returns.
Problem 2. By online, I mean just what I am doing now: With firefox, in adobe forums. During or after, won't play, video OK when scub but no sound. Again changing sequence seems to temporarily solve problem. Maybe that's all I can hope for? Ugh!
Something weird does seem to be going on. At this point, the best I can suggest is to maybe update your audio drivers.
Also, it's important to note that PP won't keep playing when you switch to your browser. That part is normal, not an issue. However, it should certainly work fine once you switch back.