Good questions so far! I'd also ask questions about the future after L3. Such as how many hours for each level. Approximate percentage of kids who have to repeat levels. How do they do move ups (additional criteria beside USAG min scores). Price increases associated with each level. Ask about the balance between family life/gymnastics. Do they encourage families to travel during the times the gym is closed and/or occasional missed practices for birthdays and other special events.
My opinion is that kids repeating L3-L6 should be the exception vs the norm. My other opinion is that family time and time with friends for special events should not be entirely sacrificed for gymnastics. Minimal absences is important but it's a balance too with 'life'. I didn't realize how quickly my DD would be a higher level optional. When you are a L4, L8 seems so far away but it goes quick! This sport has a way of sucking up family energy if you allow it which his why I suggest asking questions to make sure the gym's philosophy is aligned with your family values and attitudes with how children should be treated.