1. I completely understand the issue with Twitter account credentials. That's why I kept it with minimal requirement - provide it only when you want to Post, Retweet or Reply. When I say we don't store your credentials, I do mean it. That's why I ask it every time it is needed. But as you said, once Twitter fixes it using OAuth or so, definitely I'll support it.
3. My idea was to keep the domain name short and find the one which is available :). So its' mix of Tweet + Thought = Tweeght.
4. I've seen many people just post their insights, interesting observations, inspiring quotes, etc. So is the idea :)