Nastursiums could work. They are quick growing and I've noticed some self seeded ones just germinating in my garden
Lily pilly, I'm allergic to eggs and have found an egg replacement product that really works, I use it to make quiches. It's Organ No Egg and can be found on the high street at Holland & Barrett
I wouldn't repot it while it's flowering as I would worry about breaking the stems.
It could be a Miscanthus looking at the leaves
What sort of plant is it?
Tomato food would be better as Miraclegro has a different balance of nutrients. The potted plants have a limited root space so need more feeding and watering than those in the ground.
The leaf shape is very similar to an Aubergine.
I'd keep it as it will die in the autumn anyway. If you have small children it would be wise to remove the seed pods that have grown.
I think you need to talk to a solicitor or Citizens Advice Bureau to ensure you get the correct advice. You may also ask a builder to take a look to check that you are right to blame this rockery although it does seem likely. If you build an extension against another property you need to get a Party Wall Agreement in place first so I doubt what they have done is legal
The RHS recommends composting for at least 12 months.