1) How do I confirm the Bitcoins have been transferred to my public key without connecting it to the internet ?
2) What's the process when I want to sell them? I import the key manually by typing into Multibit, is that so, but there is only an option of Importing a file.
1) You can check balance of address with any system who has downloaded full blockchain. Simply check it on blockchain.info
If you have wallet in blockchain.info ( not your original wallet you want to protect, but just spare one without any balance ) you can add watch only address in that wallet and you will receive notification of balance change via email from blockchain.info, cool isnt it ?
2) Import depends on your export. If you have exported wallet file from Multibit, you can import wallet file to it. If you have just your private key, you can import it to bitcoinQt, blockchain.info any where. It will simply add that private key to current wallet.
You will always need private key of address if you want to spend balance from that address. If you are paranoid, you can use Armory and create offline wallet. You can create a transaction from your offline Armory, copy it and broadcast it with online Armory
Regards