Regarding those sticky keys...
These are very sensitive to humidity changes...
The balance hole (pivot point) in the key can swell and pinch the balance pin and the top of this hole will have a felt lining (bushing)......and the front of the key will have a bushed (felt lined) hole which rides up and down on another pin.
These holes can be 'eased' with a small reamer for the wood or a smooth metal pin the same size as the balance and front pin.

This is the only movement there is in the whole action as the tangent, which hits the string is at the back end of the key....nothing else moves...that's where it will be sticking...unless the keys have warped a little and are binding someplace along the length.

The solution...

Figure out how to remove any casework that is in the way....remove all the keys in order...and number them !!!
Then clean the pins with a cloth and alcohol to remove any stickiness (if any).
Spray the pins with teflon powder if you can find it (not WD-40)...or merely polishing the pins could suffice...
Then put the keys back one at a time and test how it moves over the balance pin and ease the holes until the key drops under its own weight...DO NOT OVER EASE HERE)...
Then try playing it before putting the case work back...this should work....

Good luck...
Hope that all helps.

Peter Sumner
Concert Piano Technician
Redwood City
California