1. In the long term, not really but obviously I want to save money where I can.You'd have to answer a few questions IMO. Is the cost a burden to your budget? How often do you dive? Does the stock mouthpiece ever bother you/is it comfortable? Do you plan on diving for many many years?
If cost is a factor, the one you have chosen is a great solution. So many regs are manufactured by just a few companies nowadays. Two different brands can have virtually identical guts.
If you dive a lot, then you should absolutely buy your own. Adding up rental costs will let you know where the break point is.
With your own reg, you can install a form fitted mouthpiece. I did this many years ago and it made diving much more enjoyable.
If this is a sport you plan on staying with, get your own. If it's a passing fad for you, just rent.
2. Mostly a vacation diver (think 3-4 dive trips per year, 2-3 days diving each time) and MAYBE I'll try diving local once a monthish.
3. I'm not really sure on this one. I guess my jaw has been a little sore sometimes.
4. As of right now, yes I plan on diving for years to come.