Depending on how the CEO will introduce me to the team, I'm either the boss, am respected by default or another team member with no authority at all and can't r

Depending on how the CEO will introduce me to the team, I'm either the boss, am respected by default or another team member with no authority at all and can't rely on status to move things forward. Hierarchy is extremely important to this culture. You really shouldn't sign any contract without knowing your compensation, role, goals[1], and position. It sounds like you really don't have a handle of what your exact position is and the role you will play is really dependent on that item. It might be impossible to achieve if you are relying on making a logical argument to carry the day. 1) some folks would rather say "deliverables"