And that same other ship could fire upon a enemy vessel from multiple angles at the same time?
Not really, while it's possible to to conduct a battle in that fashion, it would a fall back option of last resort. Again neither EMH understood the ship or tactics, they
had to use the automated system.
It's like the Enterprise's sickbay, there was a actual doctor (Beverly Crusher), so they didn't use the ship's EMH. But if there were no doctor in sickbay (like no Captain on the bridge) then you would employ the fall back option. But that wouldn't be your first choice.
No, even through the saucer did not fire on the Borg cube, it was part of the attack. Both a feint and a demonstration, even if the enemy isn't directly engaged, would be a aspect of attack. The events of BOBW part two,
was an example of a multi vector attack. Although we could likely drop the word "mode."
The Prometheus bridge has six wall stations (four with chairs), and a dual console in front of the command chair, plus the Captain's chair itself. It was designed for a normal sized bridge compliment.
The Sovereign Class was contemporary to the Prometheus class, it's design would have had access to the same generation of automation technology, the Enterprise E carried a full crew.
In one of the TNG episodes (I want to say "Haven"), Data was prepared to take the Enterprise to the Neutral Zone, with himself the only effective crewmember. It's possible that any competent officer could have done the same. In fact supposedly the entire Enterprise can be run literally from a single handheld PADD. So the Prometheus ability to be run with automatics isn't unique among Starfleet vessels.