Determining brand and manufacturer will be essentially impossible. These engines are manufactured by several factories in China and assembled and sold by small mom & pop companies under various brand names. Some distributors also name them with their own logos and/or stickers. To be absolutely certain of the displacement you'll need to remove the cylinder head and measure the bore and stroke. An easier way and usually accurate is to check the cylinder stud diameter. Typically the smaller, 49cc engines will use a 6mm stud whereas the larger engines have 8mm studs. If you have the chrome acorn nuts on the cylinder head, the larger engines will require a 14mm socket. I'm not sure about the smaller engine nut size.
The NT designation tells you that you have a good carburetor. The NT is the simplest and easiest to tune over several others available.
As for "tune ups" There isn't much to do to a 2 stroke engine. Keep the fuel clean by using a good in-line fuel filter betwen the tank and carb and run good quality 2 stroke oil formulated for air cooled engines at a ratio of 32:1. Keep the air filter element clean and occasionally open the right side gear cover and apply just a dab of grease to the gear teeth. Go easy here, don't use too much grease. On the other side is the clutch actuator. There are three moving parts that require periodic lubrication. The cam inside the cover, there is a pin which protrudes from the center of the drive sprocket and a ball bearing that is behind that pin.
Other than that just the normal bicycle maintenance is required; wheel bearings, chain lube and maintain your brakes.
Have fun, ride safe.
Tom