1. It will be UK.
Applicants are instructed to indicate that their education was completed by correspondence by typing in brackets {by correspondence} on the same line as the education institution name found in the Education Background Information tab of GCMS. The discretion remains with the...
The highlighted text itself explains why you are not able to book the appointment. They are not offering appointments for PR applications. The expiry on your BIL does not matter due to the closure/restrictive working of VFS.
Contact your panel physician and see what is the further information required by them. In most cases, they are just additional tests and there is nothing to be worried about.
It's better to get married before landing. You will need to add your spouse and wait for a new PPR which will include both of you. Personally, I prefer this approach rather than spousal sponsorship later on.
Are you planning to sponsor your spouse or planning to include your spouse in your PR application? Also, why did you register your marriage under special marriage act?