Maybe you should Google the department of land transport requirements for getting a license. Typically a doctor's certificate a residence certificate from immigration passport copies your old license blah blah blah, whether or not you can get a residence certificate without doing 90-day report is immigration office specific, check with your local office
You'll likely need a copy of the tm30 when you go report in person, your landlord doesn't need to report every month just because you pay monthly rent, they report only when you come. But for instance if you went away and stayed in a hotel somewhere for a week and returned then they would report again. With some offices you don't need to report again when you've traveled domestically but anyway it just saves a lot of possible hassle to do it.
Not enough time unless you can change your flight. The good thing about applying in the UK is your 500k doesn't need to season, if you come back to Asia and go to a nearby country to apply they're going to want to see it seasoned for at least 3 months.
you can do a test/dummy application, just don't pay or submit it. Then start another real application to complete and create the application. The dummy application will automatically be removed after a couple weeks.