It is true. Dulcimers are diatonic instruments meaning they can't play sharps and flats. If you add strings differently tension-ed strings, you will change the tuning.
It depends. If your instrument is in good shape and the neck is not bent out of shape, you don't need to replace them very often. Depending on how much...
I say you should use only one, especially if you don't have enough money for two. Just wash them thoroughly after every use so your makeup doesn't mix!