Segwit Bitcoin Transaction Signing
Yes
Most of crypto-libraries have the verify method. You can pass the compressed public key as an input. BTW, it is possible to recover Y part from compressed public key
No. For multisig P2SH (and any other type) we (a)calculate the digest, (b)sign this digest with private keys and (c)create the final transaction from all parts. We do not need to use any signatures on step (b) as a source for calculations



  Any other thing that I should look when signing a transaction?


How to redeem a basic Tx?