Where T is a moment in past time, "since T" means from T to the present.
A clause in the perfect tense refers to some state of affairs which started in the past and continues to the present, or to some past event with present relevance.
- I have known her since I lived in the street.
"I lived in the street" is in the imperfect (simple past, preterite) tense, so the writer implies that they no longer live there. They have known this woman since some past time when they lived in that street. In particular, they have known her since the day they moved away from that street.
2a. I have known her since I have lived in the street.
If the writer no longer lives in that street, "have lived" is the wrong tense, and the writer should use version 1 above. If they still live there, and want to say that they've known her for the whole time they've lived there, then they need to phrase it some other way. For example:
2b. I have known her since I moved to the street.
2c. I have known her all the time I have lived in the street.
Now for your third and fourth examples.
3a. We visit my parents every week since we bought the car.
4a. We visit my parents every week since we’ve had the car.
These are wrong because you are trying to combine statements about present habit and about something you've been doing from some time in the past. You can express the present habit, but then there isn't a relevant past action:
3b. We visit my parents every week.
To be more specific about when it was that you adopted this habit:
3c. We have visited my parents every week since we bought the car.
3d. We have been visiting my parents every week since we bought the car.
And 4 is wrong because "since" doesn't work with a state of affairs that is still true at present.
