Hi, Gretchen. No version of Safari later than 1.3.2 will run in Panther, and it's a bad mistake on Apple's part that the Safari 3 installer is perfectly willing to run and install an incompatible version of Safari on your unsupported OS version. I suspect all the other problems you mention may be due to changes in the support files that Safari and several other applications use, which the Safari 3 installer has deleted or replaced with incompatible versions.
If you don't have your hard drive backed up in the form of a bootable clone that was made before you applied the Safari upgrade, you may need to repost in the Safari forum area to ask how to recover from the erroneous installation of Safari 3.
I can't give you any advice at all about MobileMe; I know nothing about it. But I know you can download and use for free several other web browsers that are substantially newer and more up-to-date than Safari 1.3.2:
Opera 9.51.4886
Camino 1.6.1
Firefox 2.0.0.15
These all run in Panther.