1) Yes, if you give people the bitcoin address corresponding to the paper wallet then they can deposit into that address.
2) Importing the private key into another wallet is probably the easiest way to spend from a paper wallet, but once you have done this, the wallet is less secure so it's best not to use it again.
3) You can type the bitcoin address into http://blockexplorer.com/ to see all the transactions that have happened involving that address.

My top tip is to try out using a paper wallet with a small amount of bitcoin and check that you can retrieve it after you've sent it to the paper.  After you've checked the process, send larger amounts to new paper wallets for long term storage.

You can actually split the wallet up into pieces such that you need some pre-defined number of those pieces (for example 4 out of 6) to reconstruct the key https://bitcointalk.org/index.php?topic=104086.0