I have games downloading onto my ps4 in Europe and am selling the system and buying a new one in the USA because we are moving there. How do I access the games I bought on my first system as I want to sell the actual console. Do I lose all the games I have already downloaded?
You will need to download them to the new console as there is no option to transfer games. Once you sign in to your new console with your old account, you should see all of your purchases in the library. (The far right thumbnail.) Note that you will need to use your original account. (You can use a non-US account for gaming even if you are physically in the US. There is no region locking for games.)
Note that there is no need to sell a console in Europe and buy one in the US. A console purchased in the US and a console purchased in Europe are physically identical except for the plug. (https://www.amazon.com/Sony-PlayStation-Power-Adapter-Cord/dp/B00HALLIUS)