What if I already did it? Shall I take it as my current address 19RidcN96xgXkWi8gDwxcmbjjdjfrxpxvv's privkey has been compromised? Should I still use that address or change it to another one?
If you input your private key directly in the site without downloading the webpage and running it in tails then yes, consider that address compromised.
As well, if that's not the site I should be using, please take me to something that's trustworthy and could get me a SegWit address.
Electrum wallet can generate native segwit addresses (Bech32)
If you want for mobile then Samourai wallet can do that also.
I use GreenAddress and GreenBits apps, they've currently given me with addresses starting with a '3'.
Addresses that start with 3 are P2SH addresses, Segwit addresses are P2SH-P2WPKH addresses so they start with 3 also.
IIRC Green Address and Green Bits addresses are multisig Segwit addresses.
Are these addresses just for one time use or can I use them normally just like I use my Legacy address? As I won't be holding private key of such address, is it safe to keep my funds there?
You can use ANY bitcoin address as much times as you want as long as you hold the private key.
It is just not recommended because of privacy reasons and the hypothetical future when muh quantum computers will break bitcoin security.