I'm not running this personally, but I can answer your questions:
1. Is it a faster more stabe rom
Time will tell. It shouldn't be any less stable as it doesn't replace the current software, just adds to it. Though there's no technical reason for it to be considerably faster, lots of users are reporting simply rooting the phone and removing some bloatware makes for a significant speedup. This still could be the 'this is so damn cool!!111zomg!!' placebo effect, but my rooted phone does seem a lot faster and more stable.
2. Does it get rid of the HTC supplied messaging app?
Nope, it's still there with all of it's flaws. Since this is a binary app included by HTC (ie we don't have source code to recompile it), someone will either have to a) write a custom Messaging app that integrates with Sense properly (unlikely), or b) wait for HTC to release it's fixes, then incorporate them into the custom ROMs (more likely)
3. Does it dramatically improve battery life?
4. Does it fix all previously known bugs, for instance dropping mobile internet connection status for no reason?
Probably a no to both of these - again since it's not replacing any software, only augmenting it. It's still the same Hero with all it's quirks, just made better by rooted software and more open software choices. What probably
will increase your battery life is removing some of the stock Sprint / HTC applications you don't use that are always running in the background. Fewer processes = less CPU cycles used = longer battery times.
