on the first issue, I think your man did a great job in explaining your stance on the parking situation, too bad if it puts their noses out its your spot, you pay for it as part of your leasing that property, end of story. IF they happen to park there in future simply tell them the next time it happens that you will call a tow company to remove it, or the police!

on the second issue - If you see the lady again and again she tries to engage you just "remind" her about your dog (I told you last time T is not a social dog PLEASE keep your distance) and if it continues just walk pup at different times and see when she is or isn't at the park.