Need some help and advice. Ever since I got a twitter account, my SMS alert alarm is always going off. I can't silence SMS messages as I use SMS regularly for other purposes. Is there a way of making SMS messages from "twitter" silent?

Yeah. You can set up a profile for Twitter. Call it "Twitter" and set it up the way you want. Then from the profile menu, hit the menu key, and choose to make a new exception. Call the exception Twitter, and choose to use the profile you just created and named "Twitter." That should do it!