I have an AT897 and an AT825.

1. These mics do not have a power switch. If I leave the battery in while it is in the case and not being used, is the battery still draining? How long will it last under these circumstances?

2. Do most people leave the battery in or take it out?

3. Sometimes I need the battery, like when I plug it into my iRiver. If I accidentally leave battery in and use the phantom power on my DVX as well, will this damage anything? Other issues?

Yes it still drains. The AT897 is listed as 1200 hours, the AT825 is 1000 hours.

I put one in if I need it, which is rare. I take it back out when I know it will be several days before it's used again.

It won't hurt anything to have a good battery in with phantom on.

Some brands of mics state that having a totally dead battery in with phantom on will affect the mic's performance. I don't remember if I've ever seen that caution with AT mics though.

Just make sure to clean the ends of the battery with a soft clean cloth before you put it in the mic. Even a fingerprint, especially when it's on an electrified metal surface will eventually block enough voltage to make your battery appear weak or dead.