If you are confident that the strata plan clearly shows that the place you are parking in is not part of the common property, then I would write a brief response that says just that. I’d copy in the executive committee too since they might be fired up to fight a battle that they don’t realise is outside their area of responsibility.
Assuming you are correct, I suspect that the strata manager is being lazy and has not consulted the strata plan. A strata manager should consult the strata plan as their first port of call on any question like this but sometimes they don’t. Eg. Our OC had a serious issue linger unresolved for years because a former strata manager had advised an executive committee that an area was not common property when it was.
As for anonymous notes, not much you can do. If you believe you are parking legally on a public road you could report the letting down of tyres etc to the police. If you are not parking legally, then you probably don’t want to draw attention to that. Nonetheless, it is not the responsibility of the Owners Corporation to police parking that is not on its common property, though the OC or any individual could make a complaint that could lead to more frequent inspection of the area and parking fines. If the area looks like it was intended for parking, you could write to the local council and ask them to put in signage that would make it clear that it is a legal place to park.