Here are a few bathtub drain schematics and bathtub plumbing diagrams. Fairly simple drain system. If you have to hold your drain lever down for the tub to drain it is more than likely the tension spring on the back of the overflow plate. You can replace just this plate at your hardware store for a few dollars.
Frozen drain levers are usually from the corroded bucket gate at the bottom. If you can pry up the bucket with the attached rod, you may be able to clean it up.
Sometimes drains become really difficult to remove and require a friction drain removal tool. These are handy when the inside cross piece of the drain is broken off or has corroded away.