That is a Hardtop........ big difference as the sedans have an ugly roofline, there is no style. In fact, I'd rather have a 4 door hardtop than a 2 door sedan. The 2 door hardtops have the low sleek roofline and are of course the most desirable. The hardtops (2 and 4 door) were called Lancers and have the Lance emblem on the quarter panels. So your car is technically a Custom Royal Lancer.
Lots of info at Forwardlook.net
Category & forums listing - The Forward Look Network
The bolt pattern is 5x4 1/2", left hand thread on drivers side, and same size wheel studs as the 60's muscle cars. The rear end is an 8 3/4, but the hubs are a tapered fit to the axle, so you have to use a puller to get the drums off.
The Custom Royal is the top of the line model and should have the Torqueflite transmission, the other transmission available was the 2 speed Powerflite. To start the car with a Torqueflite, you press the neutral button, I always thought that was cool. The engine is a 325 Poly and can either be a 2 or 4 barrel
Common rust areas are floors, trunk, rockers, behind rear wheels, and the top leading edge of the fenders due to no splash guards.
A common problem with cars of that era are the front brakes pulling to one direction or grabbing. I've read that the reason is due to the shoes have to be adjusted just right and many people don't know how including myself. The fronts have dual wheel cylinders so each shoe has it's own wheel cylinder. As far as poor quality cars in 1957, that is a non-issue now that it's 60 years later. Especially if the car has had a full restoration.
If it's as good as it looks in the picture, I'd buy it for $10K. In fact, if you don't buy it will you give me the sellers contact info?