How to approve my Mac Air to be able to approve approval codes so that I can update my Apple ID settings?

how do I do get this information so that I can get everything updated and be able to get information that I will lose if I have to reset my Apple ID and whatever else it tells me that I will lose if I do this or that. I do not understand everything that I am being told. I have read something about turning off the two step authentication in order to be able to be able to get a code to approve each of my devices. Please help me to know what I am doing and how do I get each device approved in order to be able to get information from both devices. I have asked this same type of question yet I don't understand how to do what I have been told. I have signed into iCloud on both devices and it tells me on my iPhone that this may take some time and all I get is the spinning never ending circle and it gets so frustrating that I just want to give up. When I am connected to the internet it will tell me the same thing, waiting to get a code to approve this device. When I log into my iCloud on the Mac Air, I see that I have an email that shows that it hasn't been approved, it is a gmail account and when I try to change the password for that particular email, it changed my main email address account and then I get all confused again. Is this something that will have to be approved before I can do any kind of approval? I had to create a new email address when I went through my divorce 3 years ago and I am not able to get all of the text messages act. I wondered if the apple assistant that was helping me when I got my replacement phone had me to delete a certain idmi # on my laptop, would this be a reason that I can't get an approval code, what is the deal about the whole approving each device because I can't get it to give me a code to approve each device to receive an approval code? I have no idea what to do and I can't update my iCloud settings if I can't ever get an approval code or if it says both of my devices are approved to receive approval code yet I never get the code for my iPhone , all I get is waiting while watching the never ending spinning circle waiting and or it says this may take a while at the bottom of my iPhone . I turned off find my iPhone once to check something for a friend and then it tells me that my Mac Air wasn't approved to receive codes, so I hope that I can get some help in order to get this information updated asap. I need to get this updated as soon as I can, I need to have some information for court purposes and I have been waiting forever to get to update my iCloud settings.

Please help me if you can and if you understand all that I have typed up to send to you to get some help. Thank you so much, I appreciate your help in advance for your help. I may need to get step by step instructions in order to be able to understand the information that you may send me.