Yes, the lat dorsi is the muscle from the back. The implant was to match the other side (which was reconstructed back in 2003 with a TRAM). I have been unlucky enough to go through this twice!
I'm not sure how you would go with future screening with an implant on the other side.....I never had to worry about that but hopefully some of the other girls can help you.
I don't have any testing any more as I no longer have any breast tissue. It is a bit daunting when no-one is looking over you....I still have to have checkups every year with my oncologist but it is just her feeling my reconstructions and asking how I am feeling - no tests, blood tests or scans.