Is multisignature usable, if so what is the business process
Is it practical to use multisig on a Core wallet?


yes, but for sure it depends on your level of comfort. It's not (yet) plug'nplay :-) See also the example from Gavin at the end.


  If so, in simple two of two scenario, what is the process of
  generating a transaction?


see example.


  Can a third party holding neither of the private keys, propose a
  transaction for the two signers?


yes, a third party can create the transaction, and post it to the network (he would need to have the bitcoin addresses of the other  participants, to create the redeem script).


  Do they all need to use the same terminal?


no, not at all. I have done creation of the funding tx on my online system, and signing of the spending tx on an offline system (cold storage). 


  How does a signer know a transaction is waiting?
  there is no protocol inside bitcoin for "notification". When you prepare a multisig, you need to have a different communication channel than the bitcoin network, to inform on necessary signing. 


Example:
https://gist.githubusercontent.com/gavinandresen/3966071/raw/1f6cfa4208bc82ee5039876b4f065a705ce64df7/TwoOfThree.sh

btw: next to the examples to bitcoin.org, Andreas book "Mastering Bitcoins" (2nd edition) has many references to multisig, and it's wortwhile to read. It can even be found online.