Multiple Qualifications

Our club has 3 teams - 4577A, B, and C.

If we enter 2 regular competitions and 4577A wins both of them, then does this mean that we can enter 2 robots in states or can we only enter 4577A?

In other words, are qualification spots earned for the team that won and that team only, or are all spots granted to the club for them to be able to do whatever they want with them?

They are only granted to that team. If you qualified 4577A, you could only send 4577A to state/worlds.