To answer your questions
1. You can only do that if the Mortgage lenders agree
2. Yes since you have not remarried a court order is still an option
3. You can indeed claim credit for any extra value that came from the work that you did and for any debts that you paid off.
More generally the fact is that you have three choices.
If you wish to keep the mortgage as it is you can postpone arguments about his share until the mortgage is no longer the best one available.
Keep careful accounts so you simply do nothing until he actually contacts you
You can take action immediately. You will first have to attend a Mediation Information and Assessment meeting to see if the matter can be agreed - but if not then you can apply to the Family Court using a Form A and paying the fee of £245
The Court will then decide what share you each have BUT will almost certainly order that you pay him his share (such as it might be) immediately and obtain his discharge from the mortgage - which may or may not mean that you can keep your current mortgage
You can arrange the remortgage and see if he will simply accept that he has been released from the mortgage!
Please ask if you need further details