You might get different opinions on some of these, but here's my take.
It is three years since I have been here. / It is three years since I was here. -- The use of "here" implies that I'm in that place now, and I understand both these to mean "I'm here now, and I was here three years ago, but I haven't been here at any time during the intervening three years." Some might argue that it's more correct to say: It's (been) three years since I was last here.
It is three years since I left here. -- Here there is more of a sense that I inhabited or frequented this place (say a house, or a town) until three years ago (then I left, and now I've returned again).
We visit my parents every week since we bought a car. -- I think it should be "We
have visited my parents...", though I suppose "We visit" is passable in everyday conversation, even if strictly speaking it might be grammatically suspect. This sentence means that we bought a car at some time in the past, and every week since then we've visited my parents. "We visit" implies that this pattern of behaviour will continue into the future, whereas "We have visited" is neutral on that point. (It is also possible to interpret "since" as meaning "seeing as", as explained below, but this interpretation doesn't come very naturally to me here.)
We visit my parents every week since we have bought a car.-- "Since" in the sense of a duration of time doesn't work so well for me with "have bought", so here I tend interpret "since" as meaning "seeing as". In other words, having a car enables us to visit our parents. (If the writer didn't mean that, then why did he not just say "bought"?). This changes the meaning significantly.