Hello!
The freelancer should have the license, but if the company you are working for wants to buy it for you that's OK.
If you are a business of any size or type, you must buy a business license. This means if you are registered as a business or freelancer in your country with your government. If you are operating as an individual with no official business registration with your government personal edition is fine.
Published games are unaffected when plans expire - you would only need a plan again if you need to make changes to the game/re-export etc.