Say right now I'm in my Multi-bit Wallet and I have 1 BTC, and I haven't done the "export private key option" yet.
If I want to send my 1 BTC coin to another address...does it just "work"? Or does the program ask for a password/private key for the send to be complete?
I don't use MultiBit, so I don't know if MultiBit has any sort of encryption or password protection. All the wallet programs that I use encrypt my private keys, so they won't send bitcoins unless I supply a password.
Is the "export private key option" only if I want to access my coins at a friend's house on his Multi-bit software for example by using the "import private key" option?
The main purpose of exporting private keys is to allow you to rebuild your wallet if it is destroyed. While you could import your private key on a friend's MultiBit at his house, he would then have access to spend your bitcoins. The bitcoins associated with the bitcoin address that was created from that private key would essentially belong to your friend (as well as any bitcoins that are sent to that address in the future).