If you are a "DAA" player, you tune the Bass string down the half note, then use the same "4th fret" on the Bass to get the others. (Relative tuning works similarly for other tunings.)
If you go back to Jean Ritchie's Dulcimer Book, the basic tunings were a whole step lower - Cggg, CGcc and so on, so lower tunings are more traditional.
Yes, that's correct.
To sound good, you'll need to tune your other strings down the same amount (a half step, or a whole step).
Keep in mind that some note intervals have only a half step between them to begin with: E to F, and B to C. Thus for example a whole step lower than C is Bflat. I find it helps me to remember which are the half-step intervals by thinking " E at F ood, B e C ool". Also, in most music situations, people call "Dflat" Csharp... different name for basically the same note.
Unless you are playing with other people, or practicing along with a recording in a certain pitch, there's no reason you can't tune your whole dulcimer down a step, for various reasons.
What are you up to? 
Hello kids. I know I know not Jon again. I have a tuning question. For example, let's say You want to tune your Bass string down a half step. Do you tune it to D flat ? And tune it to C for a full step down?
