Beth,
First, this post in my traditional playing Blog may help you tune:
http://dulcimer-noter-drone.blogspot.com/2010/12/what-notes-do-i-tu...
I will try to answer a few of your questions:
And, I understand it, the melody line is played on the string closest to one's body when held on the lap. And, that is string gives the highest notes. (Or those two strings if one has double melody strings.)
Correct.
Now, If I'm right in this, the other two strings are both lower than the melody string.
Correct.
Here is my problem. If I tune to DAaa, the aa strings are my melody strings. I have a very limited range left in my voice. a below middle c to c above middle c is the best I can stretch on a good day.
Is it possible to get strings for the melody that will tune to low A? And would it have to be a wound string?
You will actually be tuned to DAA (or DAAA), not DAa or DAaa. The melody string(a) in this tuning will be tuned to the EXACT SAME note (A) and in the SAME OCTAVE as the middle string A.
Most importantly- if tuned to DAA you will usually be playing and singing in the key of D , not in the key of A .
People normally dont put heavy low wound bass strings as melody strings.
Or should I just tune to DAaa and sing an octave lower than the notes I'm playing?
Tune to DAA (since double melody strings are usually tuned the same as a pair, we usually just give them one letter, not two, when naming the tuning) and you'll be in the key of D (the melody will be based around the THIRD fret, a D note, not based around the open melody string which an A note). Sing in the key of D, in whichever octave suits your voice. Or sing a harmony to what you are playing. Or, tune all your strings DOWN one step from DAA to CGG and you'll be playing and singing in the key of C instead of D, which might be easier on your voice. Lots of us do this.
I suggest you just start in CGG and learn to play a simple song like Hot cross Buns or Frere Jacques, rather than trying to transpose guitar or uke music right off the bat. You need to understand the very most basic simple concepts of tuning and playing the dulcimer, without worrying about what you do on other instruments ...for now.
I give a lot of this kind of advice in my noter-drone traditional playing dulcimer Blog, here: http://dulcimer-noter-drone.blogspot.com/