Fwiw the PoS network is already running, with $6 billion staked and 100,000 validators. Migrating the rest of the network is relatively simple, they're just being really careful with it.
Yep it's another blockchain running in parallel, called the "beacon chain." Anyone can deposit ETH in a particular contract on the main chain, and the beacon chain will read that and credit them ETH on the beacon chain.
The quickest migration is basically to upgrade both clients to talk to each other, and for the old client, instead of choosing blocks with the highest hashpower, choose blocks whose hashes are chosen by the beacon chain. Details here: https://notes.ethereum.org/@vbuterin/B1mUf6DXO