1. Will Schnorr signature nullifies the threat of quantum computing?
No. Because Schnorr signatures use elliptic curve cryptography (to answer your third question as well) - secp256k1 group for Bitcoin specifically, and they rely on the discrete logarithm problem being hard in that curve, a quantum computer might be able to solve it and thus break Schnorr signatures in polynomial time.
2. How are transactions going to be, will bitcoin users be able to create a multisig transaction with it and with low fee paid?
Some new multisignature schemes (Musig1/2) will use Schnorr signatures but with the additional feature that public keys can be aggregated together and have this aggregate public key put in the transaction which improves privacy. Since only one public key is in the transaction, the size is reduced and therefore less fees are paid, but otherwise nothing else changes with respect to fees.