1.  A Timpani question...

You don't mute notes that are sort of attached to eachother right?  For example, a half note followed by another half note in a measure of 4/4.  You would just let those ring together and then mute the second note if there is rest after that measure... right?  You only mute when there is rests seperating notes.. right? 

2.  Concert Bass Drum Question...

How should I know when to mute the bass drum with my leg along with my hand?  Is it just if the composer wants the sound extra muted then you do it?

I had never heard of using your leg against a concert bass. I would assume the bass is on stand? We always used the palm of the other hand against the head to mute it. Then strike the other head and quickly mute that side at the same time.... Am I misunderstanding something?   

It's kind of an old school style, but I prefer it myself. Usually the bass drum is upright, not tilted.

The left hand is used on the vibrating head to control the ring, the knee can rest against the beating head or not to control the amount of ring of that head. I like it because it gives you control over the ring of both heads.

Most school ensembles now use a tilting stand and use the left hand to muffle on the beating head. If the vibrating head needs muffling, a towel over the back of a chair is placed against that head. There is also a device designed by Tom Freer that lays on the beating head, with a strap around your neck to lift or lower it so you can use both hands to play.
http://www.percussionsource.com/ProductDetails.aspx?ProdID=255166&ID=249

Goes to show, I'm very old school....    I've never been taught or shown the "leg" method on a concert bass drum.