If a 7 year old sits on an adult's lap does he need his own ticket?

Yes

Yes and he will get his own assigned seat.

Yes only under 2 is free.

No but it's going to be tight. Once your inside you can let them sit next to you! That what I did

Depending age if not baby. Was there an no ticket for her but she is 1 in half

I'm not sure, I believe they need a ticket.