Is it a metal box, and is the box grounded? If so, the switches are
grounded (more or less) through the box.

If not, then yes, you should ground the switches. It doesn't make a whole
lot of difference; unless they get wet there isn't much chance of getting a
shock off them, but if they have grounding contacts on them, it is easy
enough to do. (even if they are grounded through the box, they should still
be grounded by wire.)

What do you mean one wire? You want to run a single wire from one to the
other and the other and then to the ground? Probably not optimal, but it
will work.

Around here grounds have to be crimped together; but any connection is
better than none.