HAO DO I KNOW I GOT COIN>?

Okay, I'm being facetious, but I've tried to inform myself through research and now I'm just going to bite the bullet and ask some very newb-ish of questions:

Using Litecoin-QT, how do I know when I've successfully mined a block?

Also, I understand that transactions often are often accompanied by verification fees.  Since I'm running the client, does that mean I am participating in the verification process?  Will I eventually start accumulating a small amount of fee revenue as well?

For bonus points:
I've read conflicting information as to whether the client needs to be open for me to receive coins.  It seems like I should be able to close it and when it catches up on the block chain, it will see I got paid.  So, which is it? Should I keep a client online if I'm expecting some coinage?