What version of Android do you have?
No, it's not normal. No, it's not the Fascinate handset as a whole. I have one and I know two others who use theirs much more than I do with little to no problems.
Yes, malware is a known issue on all mobile devices, including Android phones. Depending on where you browse and the apps you install, you can pick up things ranging from poorly written phone apps or web scripts to info-stealing phone-hacking viruses.
You also get so zealous about closing stuff that you end up shutting down services that need to be running -- or your phone will freeze!
What to try? I have no idea how knowledgable you are about your phone or thd Android system, so here are some generic suggestions:
-- Search these forums for good antivirus apps. Pick one, download it, and run it -- three times.
-- Search the forums for stopping or killing apps and services. Read and heed; act responsibly.
-- Consider backing up all your files to the card, remove the card, and do a factory reset. Search the forum to find out how.
The phone is not necessarily bad. That doesn't mean you didn't get a lemon. Many Verizon techs are pretty helpful. That doesn't mean you won't get a lemon. If you do wind up calling or personally talking to a Verizon tech, insist on one who has used the phone - not just someone who has "had the training" and can read instructions off the computer screen.