If I sweep it in Electrum, would all the alt-coins follow along - meaning can I then use the new wallet to extract any potential BCH, BTG, BCH?
No. Only the bitcoin will move. The forkcoins will remain on the previous address.
If so, after importing into Electrum, which is the easiest way to retrieve the fork-coins?
After moving your bitcoin to your new Electrum wallet, you'll need to download a wallet for each forkcoin, import your old private key in to it, and then create a transaction to move that forkcoin.
AND - would it be possible to skip step 1, meaning can I just sweep directly into a wallet?
Definitely do not do this. You are going to be exposing the private key to that address to a variety of wallets to move your forkcoins. There is a high chance of compromising that private key and putting at risk any bitcoin which are still stored on it. Move the bitcoin off that address first, and then go about importing the private key to different forkcoin wallets.