Just a few comments:

1. Don't worry too much about the tax situation until you spend more than 183 days (in a year) in the UK. At that point you become an automatic tax resident. At less than 90 days you are automatically non tax resident. In between it is quite a difficult process to determine tax residency but if it is a 'once off' >90 days stay, it is likely that you wont be a tax resident. (I am not a tax expert, but I have been 'in the same boat')
2. As a UK citizen you should have NHS coverage when you are in the UK. But of course you would have to register for that at a local GP practise (unless in case of emergency)
3. Quarantine: Yes, you will have to self isolate. You can do this in a separate room in your family's house (as far as I understand).