You are slightly paranoid (regarding 1 and 2)
Regarding 3 - it is normal.
Bikes are usually started with open throttle when the engine is warm. They are started without throttle when cold.
If my bike is parked in summer sun, I have to apply throttle even if the engine is cold. Ditto for air temperatures over 25C.
This is how automatic choke works.
Few thousand kms is nothing if everything else is fine. Do not worry and buy it.
I would personally prefer to buy a scooter with few thousand kms. First, it is already inspected, somebody has paid for first and second inspections and if there were some little glitches they are already fixed. Then, documents and paperwork for a new scooter are around 150 US$ for a new bike, and when you buy used you save that money. Finally, it is possible that somebody has already installed a topcase, such things usually "go with the bike".
5 years ago I bought my Beverly with 1000 kms on it at 35 % discount.