You need to check with both offices. Obviously you are collecting an accumulative benefit through the interstate agreement of the states and earned in the respective base periods of both.
Generally, no because they are not wage earners and are normally ineligible, like commission only sales people. They are considered independent contractors and self-employed.
This depends on the state you work in. Generally not, because some states consider the off school season as not unemployed. You need to check with your own state for criteria.