Twitter issues

Me and my fiance recently subscribed to Twitter just to leave private messages back and forth between us. It was kind of cool at first. But then it became very weird. Strange people we don't even know began "following" us. One is very persistant and has links on her site that will try to infect your computer with a Trojan Virus if you click on them. My anti-virus prevent that.

Twitter's HQ offers very little support with any issues.

Who here can share their own horrible experiences with Twitter? Is this a safe site? Or is this is a huge mistake to post on there?

Thank you.