In my humble opinion in the absence of any agreement between the two of you, the
most you could be asked to repay is the 10K he paid towards the deposit and that would be fair.
The electricals are staying in the house, you agreed to them, and you get to keep them and they do add value to the house. Extra solicitors fees should probably also be yours. Neither should come off the 10K deposit .
His name is not on the deeds so he has no entitlement to any part of the capital appreciation and the letter he signed stops any kind of argument.
It seems fair that he reimbourses the car loan payements you made for him -assuming he keeps the car
. So in my humble opinion if you were to give him any money back, give him
10K - car loan payments= his refund. (€8000?). But then again he said he didn't want any. Make him a final offer and tell him that he can take it or leave it.
For your own piece of mind, you could give him the full 10K back, even though he didn't ask for any of the money. At least you can look back on the house in 10 years and have nobody to thank but yourself.
Congratulations on breaking up. Who wants to live with somebody this mean?