Will electrum allow me to send coins to multiple addresses in a single transaction with a SegWit address, just like I do with my Legacy address?
Yes, you can do the same things with segwit that you can with legacy addresses, the only difference is that segwit transactions have lower fees.
I won't be using that address anymore, but to make everyone aware of the same, what should be done? Making a thread in Meta and signing a message with that address saying that its private key was used on a website and I believe it's now compromised, so don't send any coins there if someone asks anything by signing a message from that address. Will it do?
Yea, that will do IF the people going to send you coins check the meta section in the first place.
You can alternatively keep the private key of the address in case it's not actually compromised and you eventually receive any payments there.
But DO NOT give it out as a receiving address any more.