Can two people work the inbox at once?

Yes - your whole team works the same inbox at the same time. There is no queue and nobody has to wait their turn. Everyone on your plan shares one inbox, and you are not charged per person.

You can assign a conversation to anyone on the team, and filter the inbox to Mine, All agents or Unassigned so nobody has to remember who picked up what.

When you assign a conversation to someone else, they get an email saying who handed it to them, with a link straight to it. Nobody is emailed when they assign one to themselves.

Coasting also warns you when a colleague is already looking at the same conversation, so two people do not answer the same customer twice. That is a collision warning, not a lock - it helps you avoid duplicate replies, and it does not stop your team working in parallel.