SlamDesigns, the first two sound like it may be DNS issues. Maybe your ISP's DNS servers are buggered. Which would lead to problems with #2.
As for #3, I use Opera and sometimes the favorite icons get a little screwey too.
If you want to try good nameservers, go to this page:
http://www.opendns.com/start/ and try hardcoding their nameservers. Chances are they are better then your ISP's are anyways. Pages load a lot faster for me using their DNS entries.
If that doesn't work, you might had a spyware problem. A couple years ago I had wierd things like that happening and found out some spyware changed my DNS servers on my comp to theirs and it caused all kinds of problems.
