As an employee, you should continue to be able to fly any mission types that you have unlocked regardless of any companies you own. You only get about 10% of the mission reward but you don’t have to worry about the aircraft, maintenance or insurance.
As a freelancer, you will only have access to missions associated with the company or companies you own as well as the aircraft you have purchased. For example, a cargo company with a Cessna 172 would only have access to Cargo - Light missions. To fly Cargo - Medium missions you would need a medium cargo aircraft such as the PC-12 NGX, PC-24, Cessna 208B Caravan, or the Cessna 408 Skycourier. You can purchase multiple companies and up to about 1,000 total aircraft.
In freelance mode, trying to select an aircraft that is damaged and not flyable will result in an unexpected error trying to transfer or select the aircraft for a mission. Simply go to your HQ, view the aircraft for you company, and repair the aircraft you want to use.
“GROUNDED” is referring to the aircraft. Repair the aircraft and you can continue to use it for missions.