What is "Key Splitting"? When would I use it?
No. Multisignature transactions involve multiple keys/signatures, whereas this involves splitting up one key.
As far as I know, it's not used at all in production. There are a whole host of issues.
P2SH was created to make multisignature transactions easier to implement for e-wallet providers and merchants, and to move the burden of multisignature transactions from the sender to the reciever.
Like so:


Generate a key
Split the key up, store the pieces in different places
Put the key back together
Sign transactions


The major problem with split-key transactions is that you need a trusted third party. When they generate the key, they could secretly store it. When they put the key back together, they could secretly sign a transaction that stole all of your bitcoins.