Hot start issue, and another concern

I am pretty new here. I have been reading a lot of posts, but haven't commented or started any threads of my own until now. I just got my 2005 RX-8 in July (traded a kid straight across for my bad tranny BMW, hoping I got the better end of the deal. Now Im not so sure). When I got the car, the kid I got it from told me the starter was going out. My car was not included in the few 05's with the recalled starter that Mazda replaced. I don't know any of the history on the car whatsoever. I never noticed long, cold starts until I watched everyone's videos with their upgraded starters and 1 second starts. My cold start is 3 or 4 seconds maybe, but it starts on the first try every time. On hot starts, sometimes it can take up to 8-10 seconds to start, sometimes it wont start at all. I have watched video after video on bad starters and have noticed the same thing in every one of them. The RPM gauge acts different than mine does, and I am hoping someone has an explanation (please bear with me, I don't know a whole lot about cars, and I am a girl :wink2:). It seems like everyone's RPM gauge stays on 0 when they are having a long start. My gauge goes up to maybe 500 RPMs. If my car is going to start, the gauge will stay there until the car starts. If it is not going to start, the gauge will drop back down. There are a couple other issues I have noticed with my car: my idle drops when I am in drive, but sitting at a stop light, and my car vibrates. The RPMs drop to about 800-850, then they come back up to around 900-950. The only other issue I can think of is the other day, I backed out of my driveway and as I was backing up, the car stopped suddenly, as if someone slammed on the brakes. It did it twice (and scared the crap out of me). What would cause this?!? Any advice is much appreciated! Thank you.