Brick Garden wall

Hello, it will depend on if it is a double skin wall then yes just your side can be replaced depending on the brick bond, but if is a single skin wall the answer is no

If it is 9inch wall it would very hard to take1 side down because the mortar is to weak thats why weed growing throught the mortar I would nota temper to do this I would ask if he mind to take wall and rebuild the wall with no cost to or her if they agree get writing that they agree and sign and date it before start the wall

It depends on what side its on if its on the left hand side of you're house, has you look at you're front door, then it's you're wall including the back wall. And for the "short term" you could extend the footings and apply a skin of brickwork just on you're side. Another alternative and "longer term" is to knock it all down put blockwork on you're next door neighbours side and the bricks and bond that you want on your side and tied in with brick ties. It will also lower the cost in materials. Hope this helps you out.

Another option would be to render the wall on your side to improve the appearance

The garden walks are usually 9inch thick which is 2 bricks wide , so it’s unlikely that you can take your side down and rebuild it without it effecting the back side ( usually they are tied together with a brick across both sides called headers) my suggestion is to just simply render your side . Job done