A partial setup should not be the reason for these errors and I’d be hesitant to assume signing up for a proper account will magically fix all of them.
Without knowing what the exact errors are, it certainly is difficult to provide further advice, but in most cases these issues are because of some errors on your hosting server and they will not stop just because you signed up for a proper account.
I don’t know your host and most certainly don’t want to bad-mouth them, but I would not be surprised if one of the motivations to suggest a proper account is for them to be able to tell you look, you are on a full account now and we don’t have anything to do with that, please talk to Cloudflare. Again, this is rather an assumption but hosts very often don’t know of any issues on their side.
Before you change your account I’d really rather figure out what those errors are and how to fix them. For that I’d recommend #tutorials as well as the search here, as there are dedicated articles on each individual error code.