Hi there.
For the first, are you want to apply for temporary 5yrs Residence Card or PR as a Retained Rights of Residence?
You need to prove that duration of your marriage at least 3yrs and 1 of them spent in the UK.
1. As your ex-wife worked (part-time) and studied at the same time, you need to show that she held a CSI during her study and all of her employment documents from the date of your marriage till divorce.
2. If you have a new relationship after your divorce, of course you need to state this in your application form and a cover letter.
3. You can get your documents back through this Home Office service.
https://www.gov.uk/visa-documents-returned
Be sure that you have a Family Permit, Residence Card or another form of a Entry Clearance Visa when coming back to the UK, otherwise you may not be allowed back.