The system rusts on the inside as well, a little bit of rust can easily jam a piston, preventing it from sliding back easily when the brakes are released.
Brake fluid sucks up moisture every time you open the reservoir, so dont do it, you should be able to see the level and shouldnt ever need to add more unless there is a leak. The level will go down as the brakes wear and go back up when new pads/shoes are added.
If thats the original fluid then it is well used and time for a flush. You can also flush it every few years as you notice it go darker. An excellent way is the "one man flush", its fairly quick and easy...as long as your bleeders open, and only needs a bottle, bit of used brake fluid and a few feet of hose.
If you are lucky you can pick up some quality cheap calipers from a closeout from a place like rockauto.
To see if its sticking, put it in neutral on a slight grade, see if it rolls. Get out and check the rim temperature and compare it to the other rims, sometimes a sticking brake can get hot enough to blister a finger lol, so do it quick.