Your chain slap sounds like a dirty or partially gummed up RD. The spring should keep tention on the chain. Do a thourough cleaning with a degreaser and then lubricate well. See if that frees up the DR. Here is a good video:

http://www.howcast.com/videos/167194...ear-Derailleur

On both my older Schwinns, I replaced the stock bars with new 42cm alloy ones, for two reasons. First, they were both steel, and second, I tried to keep some consistency with the newer bikes I ride. I really like the wider bars, and I like the tighter drop geometry. For me, its much more comfortable. I got both bars on sale at Nashbar. Both were cheaper FSA, but you can look for whatever you want. Just pay attention to width. In both cases, I did not have to replace the stems.

Your vibration could be a number of things. But you specifically mention gear and speed. Is the vibration not present while coasting at the same speed?