You can use an EASA licence to fly a G-reg aircraft until 31st December 2022, after that you will need a UK issued licence.
The process involves converting your medical as detailed
here, then converting your licence as detailed
here.
1. You can use your EASA Class 1 medical until 31st December 2022
2. No, just pay money
3. Any valid rating/certificate endorsed on your EASA licence will be endorsed on your UK licence. (More details via the "licence" link given above).
You can get access to your medical records by sending a Subject Access Request to the national authority that issued your EASA licence.