Hi again.
I'll try and answer this as you have asked bits I can help with.
Healthcare. GP and nurse consultations in primary care, treatment provided by a GP and other primary care services are free of charge to all. So, if you go to visit a doctors surgery and see either the doctor or one of the nursing staff, that's free for everybody; you'll have to pay the full price of any medicines or items arising from that consultation. If you have to go to a hospital for treatment, that you have to pay for. The UK Gov has a comprehensive guide about all this; this will take you there. When you read it, please bear in mind that under your visa, you will be staying for 6 months or less.
As to who to get it from; at the top of the page is a link to our Service Section; if you move your mouse up there, you'll get a drop-down menu, one of the choices is Health Insurance; you can check that out, I don't personally recommend any of them (I've never used them). If there's nothing there you like, maybe your current US insurer will cover you (they know your health record better than most). Alternatively, use Google; here's a to a search I just created.
Applying for a visa. This will take you to the UK Gov website with the details. You can apply online; the link has the details, but it is not all done remotely, at some stage there will be form filling and personal documentation to show to someone.
Property. As you will not have permanent residence in the UK, if I were you, I'd think very carefully before I sold up my house in the only country where I had a right to reside (in your case, the US). These visas are by nature political, by this I mean that the Government of the day may change the rules on visas (the UK does it all the time), and you may find yourself needing to leave. Perhaps rent it out as an AirBnB let or similar?Â
Housing in the UK; perhaps a short-term lease (short-term can mean anything from 1 day to 50 years), it just means you never own it but do have an asset you can sell on for whatever value the remainder of the lease may have. It's cheaper than buying and if you do have to leave, it is less painful. This explains the differences.
Public transport. Like in most places around the world, transport to the remote regions of Scotland is always not what it is in the cities; some places have none at all; perhaps consider car rental for those occasions.
If you have any further specific questions, please come back to us.
Hope this helps.
Cynic
º£½ÇÂÒÂ× Team