It looks like FireFox doesn't recognize the font color ("color: red") at all, while IE recognizes it for the first paragraph only, then reverts to black. Both got the background color right.

That's pretty typical of the two major browsers. FireFox is 99% compliant with standards, while IE complies with a different 99% (or, more logically, I guess I should say that their 1% incompatibility is in different areas). In this instance IE is slightly less wrong than FireFox, but neither one got it right.

Allowing HTML in posts is a formidable technical challenge, not only because of browser quirks but because of the fundamental conflict between the software putting in <P> and <BR> tags as a convenience for the vast majority of users (who'd want to have to type those tags over and over?), and how that can mess up ambitious HTML. The general rule of thumb is that the more ambitious you get, the less likely it is to work.

One thing that usually helps is to write out your HTML all nicely formatted, so that you can see that it's correct. Then use the editor's search-and-replace function to delete all line endings (carriage returns in a bygone era when computer output devices had carriages). That gives the software filter nothing to mess with, and a solid block of HTML should generally work OK.