It is possible. It doesn't seem natural in my dialect, but it is a grammatically sound sentence.
The verb of "When is the bank opened?" is "is opened". This verb employs the passive voice, present tense, indefinite aspect and interrogative mode. An active voice equivalent would be "When does someone open the bank?"
The reason that this doesn't sound natural to me is that I expect the intransitive sense of the verb "to open" when the subject is a business or institution. A perfectly natural example of the grammar in question is "When is the safe opened?" I expect a bank to act on its own behalf, but I don't expect a safe to act at all. In my mind, there should be an implied someone or something that opens the safe.
Your last example does seem natural. The verb of "When does the bank open?" is "does open". This verb employs the active voice, present tense, indefinite aspect and indicative mode. In the active voice, the subject "the bank" performs the action. There is no object for this verb. This is the intransitive sense of the verb.
Your first example also seems natural. The verb of "When is the bank open?" is "is". In this case, "open" isn't a verb. It's an adjective. The grammar of "When is the bank open?" is the same as the grammar of "When is John happy?"