IOTA quantum resistance
Yes, it uses a Winternitz OTS scheme. It is believed that Lamport signatures would still be secure against a quantum adversary.
No merkle signature scheme used with IOTA for transactions, as the result of a number of design and security decisions, for instance, signature size. It was a conscious decision to not use a stateless merkle scheme like sphincs. So yes, you should always transfer change to a new address. The implications of reusing a private key in a lamport scheme is that each reuse halves the security level of the signature (assuming a random message).