We're getting mixed advice on whether or not a pump is going to make any difference to our water pressure if installed on the 3rd floor (the entrance to our apartment) as opposed to the ground floor. The 3rd floor is approximately 15 meters from ground level where the water enters the building. I understand that pumps are limited in the amount of "pull" they have (somewhere around 8 meters or 25 feet), but my reasoning is that the pump is not having to "pull" the water up 15 meters as the water already has some pressure behind it. If that's the case, would it improve the pressure, and by how much? I appreciate your thoughts!

When the tub on the second floor drains, my kitchen sink on my first floor overflows. They share the same air vent. Is there any way to modify the plumbing to stop this from happening? I can access the drain behind the kitchen sink drain from the garage. see attached pic of my house's plumbing. I do not have a basement. The drain from the kitchen sink goes to my clothes washer drain then out to the street.