Bricklayer

Gain permission from the neighbour and then get rid of the bush by digging it out from the root if that isn't possible then it will likely always be an issue but if can be removed and the neighbour gives permission if it's not an issue with the roots then try to either apply trellis to the brick wall when built and tie it accordingly so it grows where you want it to

I would take it down and relay it with ties or try and bore holes and put ties in accordingly but first idea is likely the best you could also render and plaster to hold it in place but ideally takes it down and if it's interior block it up with block work and render and plaster or just plaster if possible

Depends how bad the brickwork is if there's loose bricks or holes then patch these areas by either filling or taking the bricks out and replacing them then go ahead and render as long as rendered properly should be no issues

Check that the air bricks aren't blocked and check if cavities are clear of rubble this is one cause of damp in cavities about it cause is damp proof course not being done properly. also if walls are properly insulated this can also stop damp and mould and remove need for air bricks. also apply anti mould paint

If the base is okay yes just make sure its damp proofed at least but ideally would be better to go on a screed base.