Göllnitz–Gordon identities and parity questions

Parity has played a role in partition identities from the beginning. In his recent paper, George Andrews investigated a variety of parity questions in partition identities. At the end of his paper, he then listed 15 open problems. The purpose of this paper is to provide solutions to the first three problems from his list, which are related to the Göllnitz–Gordon identities and their generalizations.