Hello OP
Mine was a very different type of case (not related to property). Both sides usually pay their own costs, however it's possible for the 'winning' side to claim the costs from the 'loosing' side. I was awarded my court costs in full, which ran into the tens of thousands.
Unfortunately if the person has no means to pay, you won't get any money back (you have to pay the costs in the first instance, then claim them back). If they don't pay you can apply for a CCJ, then send high court bailiffs (sheriffs), but if they cannot find assets, the debt will be written off.
It's also best to name an individual rather than a limited company; if the company goes into administration or is dissolved, the person who owned the company is not obliged to pay the debt. I'm mentioning this as you say the neighbour is a property manager and so probably has a business. Obviously take professional legal advice if you take court action.
Regarding the boundary - have you checked your deeds, or is the 15cm encroachment based on the location of the original fence? Definitely check your deeds before going any further. If your neighbour did this, they may have discovered the fence was in the wrong place and errected their wall on the correct boundary.
If this is not the case and the old fence marked the correct boundary, I'd send a solicitor's letter to my neighbour with a copy of the deeds. I'd ask them to remove and reinstate their wall in the correct location.
With regards to your third point, I'm not sure this is unreasonable? You said "..despite paying (the neighbour's) survey fee" - this is standard practice when your proposed build affects a party wall, i.e. the surveyor costs - even your neighbour's - are down to you.
You say that your neighbour had planning permission for his extension first, is that right?
If your proposed extension is built right up to the boundary line, there might not be room for him to build a second wall solely on his side without affecting the dimensions of his original plans. If this is the case, it sounds like he's asking permission to use the same party wall for his extension.
If you don't want to allow this, he's asked for the wall to be built in London brick. I guess you have old houses and this would be in keeping?
If he can't build his own extension and your wall will be exposed on his side, I wouldn't want to be faced with breeze blocks either. It makes no sense for him to want the wall to be made with London bricks if he was going to build his own extension, as they would be covered up.
If your neighbour is keen to go ahead with his extension, sharing the party wall (that you build) might work, depending on his pre-existing plans. It would definitely save him money, so it would be nice if he made some sort of goodwill gesture.
It's not clear why you've paid your neighbour £2500 for your loft conversion. Was this figure agreed between you without any legal advice? What does this payment cover?
Rather than asking your neighbour for money (which I doubt you'd get), I'd ask for the tree to be completely removed and your garden made good. The cost of doing that could run into the hundreds. That would be an appropriate goodwill gesture IMHO.
Just an FYI - I removed my wonky (London brick) chimneys and used them to build my front wall. I researched places which sold the bricks in case I was short. Prices vary massively. At the time (2018) it was definitely possible get reclaimed London bricks for very reasonable prices.
Be careful - property disputes can drag on for years. The only winners are the lawyers. It would be much better if you can resolve matters directly between you, if possible. I know its an almost impossible challenge, but try to keep emotions out of it. Something being unfair does not necessarily mean it's against the law.
Good luck 