My Cloud is full and no matter what I delete from my mail I can not get my mail that is being sent there. I am missing my business emails. is there a way to retrieve them?

2 part question!! 😕 My icloud is full, I had 55 in storage until Apple deleted it back down to 5, and now I can not stop the the "Your email is full message" from popping up on my MacBook Pro screen every 5 minutes. I have deleted 3/4 of it however there is mail in there I'd like to keep. When they took away my storage, who knows what mail from clients I am not getting. How do I get rid of this message? Apple doesn't let you change your main email on setup it's either me.com or icloud, how can you set up your alternate email account to prevent from losing any more email?

Thanks!!