Some help understanding IMAP?

Hey guys,

I've just decided to take my 3 gmail accounts and turn on IMAP access. My main motivation for this is the fact that i'll be getting an iPod Touch in a few days and I hear IMAP jives well with mobile devices. I'd also like to be able to check my mail from my family's iMac and I hear IMAP is good for multiple computers too. Anyway, i've been toying with it for a while now with Mail.app and I have a few questions/concerns that I hoped you all could help me with.

Firstly, I'm wondering about how syncing read/unread messages works. Say, for instance, I received 3 new messages. Mail.app shows 3 unread messages on the IMAP server and makes three copies of those messages in my inbox, also marked as unread. If I go and read the ones in my inbox like I think I'm supposed to, it doesn't seem to sync back to the server that i've read them. If I read the unread messages on the server, however, they sync back to my inbox as being read. Isn't the whole idea that it syncs both ways? With the behavior being the way it is now, when I read the mail on one computer's inbox, wouldn't it still be marked as unread on the other computer's inbox, or on my iPod Touch's inbox? That doesn't seem to make sense to me.

Secondly, I can't seem to delete messages from the server through Mail.app. I'll go right in and throw messages away and tell the trash to empty. They just pop back up as if I never deleted them. Am I doing something wrong?

Well, those two are my main concerns. I guess I thought the whole idea of IMAP was so that you sorta had one inbox that synced between multiple devices so you wouldn't have to ever read the same message twice if you didn't want to. Any help is appreciated.