problems with '97 xr-7

I just purchased a 3oth anniverssary edition XR-7. it has the 4.6L V8, but it has been giving me a couple of problems.

First, it drains the battery over the course of a few days. When I jump it it runs fine, and the alternator seems to charge it back up, but if I don't drive it every 20 hours or so it tends to drain. What's the easiest way for me to locate the culprit? ( I have an inkling it may be the after market alarm or the remote start... how can I be sure?)

Also, when I'm driving it, when going around 35-45 MPH if I take my foot off the accelerator, the car lurches, almost as if in a down shift and my RPMs will drop suddenly, it only happens for a second but it's certainly noticeable to myself and passengers. What could this be?

same car i have-and sounds like the same problem! right about 40 miles per hour steady speed seems like it tries to shift back and forth i came across some sort of maintence notice from ford here is the linkhttp://www.mn12performance.com/mn12-techinfo/tsb/TV1111.pdf something about the 1-2 shift accumulator bore scuffing the link is for techs how to inspect and replace sounds like it is not too bad drop the tranny pan for acess please let me know how it turns out [email protected]