A- The snare heads are usually tuned much tighter than the toms. The reason is twofold. First, the sound usually associated with a snare drum is a tight, bright one, not long, sustained resonance, like a tom. Second, for the the snares to be responsive to bottom head, it needs to be fairly tight... really tight.
B- The bottom head should not be at the same relative tension as the batter head. In order to reduce resonance, and to help reduce sympathetic buzz of the snares, you want a good separation between the top and bottom heads. Sympathetic buzz is when the snares "sing" along with the bass guitar or your monitor speaker. Through experimentation and the advice of some other experienced drummers, I have come to the conclusion that the snare-side (bottom) head of a snare drum should be tensioned extremely tight. Don't be bashful about this. Crank that puppy up very tight. Then tighten it some more. :-) This really helps make the snares very responsive and articulate.
C-
Snare Bed: The bottom bearing edge of a snare drum, has two dips or cut-outs
in it, where the snares come across the head. This is to allow the snare
wires to push up into the snare (bottom) head. Because of this, it is difficult
to get even tension across this head. Don't worry about it. Without even
tension in that head, it will be less prone to sympathetic buzz, because
it won't have any specific fundamental note.
Don't be afraid to tighten the 4 tension rods that are on each side
of the snare wires, tighter that the others. This will help with
snare response, and help cut down on sympathetic buzz.
For most styles, you want the snare-side head very tight. Not only does it give you that nice crack that most of us love, but you get the added benefit of greater response from the head. Loose snare heads have a place, too. You get that soft, almost legato, snare sound that sort of goes, "poof." The theme of all this is to suit yourself.
D- Adjustment
of Snare Wires: In general, you want to have the snare wires as loose
as they can be without sounding sloppy. Start with the snare strainer
loosened all the way. While striking the top head, slowly tighten
the snares until you achieve a short snare response. Don't go much
further than this or you will choke the sound of the snares and diminish
the sensitivity. If you are getting too much sympathetic buzz, you
still have some room to tighten the snares before they choke. (see
below)
Many people stress out over sympathetic snare buzz, because the drum
makes that buzzing noise, even when no other drums are being played.
Before you decide to try and reduce it, determine if there is even a need
to. Most of the time the sympathetic buzz will be "lost in the mix."
That is, the buzz won't be heard over the rest of the music. If you
are playing soft music and the sympathetic buzz is distracting, then you
can try to get rid of it, or at least lesson it. You can try changing
the tension on the bottom head either up or down. Also try loosening
just the tension rods that are adjacent to the snare bed. People
will offer all sorts of tricks involving taping the snare wires or putting
felt or cloth under a portion of the snare wires. I do not subscribe
to these methods because they general result in reducing the snares' sensitivity.