How can I use multi signature addresses with Bitcoin Core? Using the instructions on the debug window, I created a multi signature address as below:

addmultisigaddress 2 "[\"Address1\",\"Address2\"]"

MultiSigAddress


My understanding is that one needs the private keys of Addres1 and Addres2 to be able to spend from MultiSigAddress. Is this correct?

I sent some btc to MultiSigAddress, both Adress1 and Adress2 belong to me and I can go to coin control panel select MultiSigAddress as input. It will send the transaction without any problems.

What if one of the addresses belonged to someone else? How could I use the funds on MultiSigAddress using Bitcoin Core in that case?

Thirdly, the address I created in this case is 2 out of 2. What if I wanted to create an address that is 2 out of 3? How can I create that using Bitcoin Core? Or is that only possible for multi-sig transactions?
My understanding is that one needs the private keys of Adres1 and Adres2 to be able to spend from MultiSigAddress. Is this correct?

Yes that is correct

What if one of the addresses belonged to someone else? How could I use the funds on MultiSigAddres using Bitcoin Core in that case?

You will need the private key for both addresses (public keys) in order to redeem funds from the multisig address.  So you will either need to have the owner of the other address sign the the redeeming transaction or have them give you the private key so you can sign it.

Thirdly, the address I created in this case is 2 out of 2. What if I wanted to create an address that is 2 out of 3? How can I create that using Bitcoin Core? Or is that only possible for multi-sig transactions?  

The following bitcoin core command will create a 2-of-3 multisig address, 

createmultisig 2 '["key1","key2","key3"]'


You can view the full list of commands here