Yes. The private key can be imported into any client that provides a method for importing private keys. You could then send the bitcoins from that client.
Note that depending on the client you choose, some bitcoins may be sent to a new address that the client creates and keeps hidden from you. So if you have 100 bitcoins (that were all received in a single transaction) associated with address A on the paper wallet, and you import that private key into Bitcoin-Qt to send 5 BTC to someone, then the remaining 95 BTC will no longer be associated with the address on the paper. Bitcoin-Qt will have created a new address (with a new private key) that it didn't tell you about. It will spend the full 100 BTC in a single transaction sending 5 BTC to the address you were spending to, and sending the remaining 95 BTC back into Bitcoin-Qt at the newly created hidden address.
I haven't tried importing private keys into either of those clients. What other information do they ask for? The only information that should be necessary when importing a private key is the private key itself. I've done it many times with Bitcoin-Qt.
I'm nearly certain that https://blockchain.info/wallet provides an interface for importing private keys. I know it can be done in Bitcoin-QT (although it is an advanced function requiring API calls in the Debug Window console).
No. It is in standard Wallet Import Format (WIF). Any client that allows importing of Private Keys should accept the private keys from the paper.
The private key is the only information needed to access the bitcoins associated with the address listed on the paper. Some clients might require you to store that private key in a file in order to import it, but that import file can be created at the time of importing.
Yes. Any client that provides an interface for importing Private Keys can import the private key from the paper after which it can spend any bitcoins associated with that address.
Yes. The private key is provided in standard Wallet Import Format (WIF).