Yep arrive late morning 9am or after and then go back later in afternoon the next day. Why do you have to be one of the first few at sparrows fart. Just means you pick up the visa closer to 2pm instead of 1pm the next day. I have never understood why people like to go immigration early and catch the crowd when an hour or 2 later the crowd has already gone back to their hotels. I suppose most people want to go on a day trip or tour or something for the day..?
I have BUPA UK. Not cheap but excellent. Depends on the procedures, previous hospital screening and whether the insurance company can prove they were pre existing. If there is no evidence they were pre existing then no need to mention them in the application.
If they did in fact do it, they probably would have done it online so there won't be a receipt. You will just have to go in with all the documents mentioned. If you are in the system when they check they will give you the slip and you are on your way. If not on the system then pay the 1600 and get it back or withhold it from the rent as you mentioned (as long as they agree beforehand). It is a lovely system.