Considering that those three jobs alone could add up to £12-15,000, then I'm surprised he has asked for a reduction of £5,000 only. It might simply be a case of exaggerating some kind of defect list, and plucking a figure out of the air.
Firstly, the damp-course.......... A 100 year old house would most likely have some kind of DPC. It may well have failed in places, but unlikely over the whole of the downstairs. Generally, my money would be on condensation and poor ventilation coupled with the fact that a house of this age would be constructed of facebrick or stone........... both extremely cold surfaces. Condensation is common with these especially with loads of added draughtproofing.
Garden wall ........... I would say it is unlikely that next door's house has affected this. There is no way (short of bribery & corruption) that a 90s house would be founded on ground that is retained by a 100 year old wall. You don't say how much higher their ground level is compared with yours. Nevertheless, their footings would have been at a depth certainly below the base of your garden wall. No Building Inspector or NHBC Inspector would allow building on such retained ground.
Also, there is little or no way that your wall could have been strengthened from his side. It makes no sense. Truth is ....... they probably simply re-pointed it. Just a guess of course, but if their house affected your wall, then the house would also have been affected ............ by subsiding.
Chimney ............. very difficult .......... simple job, but no certainty that next door will want to pay. I've seen cases where someone in your position has had the work done and paid for it all.
All these things need the opinion of a Building Surveyor to be assessed properly.
I'm not being much help here as I would need a lot more information to be sure. I'll stick my neck out and say that this is an Estate Agent........ he wants the house for sure ........... tradition and "professional honour" would dictate that he gets a discount ............ thus defects are sought out. If it weren't these matters, it would be something else.
If there's any substantiation for the defects, then I would say... give him the £5000........... that's cheap. If not, then holdout for the full amount, or try for £2500.
Good luck with the sale.