I can't sign into my apple ID or update the OS on my MacBook Air (13" - early 2015)

Basically, I was gifted my friend's "MacBook Air 13" - early 2015" (Model A1466) because they no longer use it and I have been stuck with a much slower dinosaur PC that at this point barely turns on. This is a big problem for me because most of my work is online. Anyways, until I save up enough money for another MacBook Pro this the best device I have. However, I am having a problem with updating the OS. It is running OS X Yosemite, which is to my understanding is deprecated and no longer supported by almost all apps/programs.

tl;dr I have an early 2015 Macbook Air and need help updating a newer OS.

More specifically here is what is going on. When I got the device from my friend, I wiped everything she had on here using the Disk Utility. I followed the instructions on apple.com and it automatically reinstalled OS X Yosemite. I found that I can't use Safari at all because the certificates are all expired, luckily I figured out that Google Chrome works but almost every website I have to bypass a page which warns me that "this site is possibly dangerous/may have malicious content". I assume it is the same issue with the certificates being expired, which I think is related to the deprecated OS (?)

I also cannot install anything from the app store or use iTunes, etc. No third party apps are compatible, and only a few of them have older versions available for download (these too are also "no longer officially supported" and may have limited functions. I was lucky to find this older version of the Google Chrome browser or this device would be effectively useless.

To use the app store obviously I need to sign into my apple ID. If I could do that then I could update at least to a newer OS that is still widely supported. However when I attempt to sign in, it tells me that my ID or password is incorrect. I know for a fact it is my correct password and Apple ID, and I have even gone through the motions of clicking forgot password and resetting it to see if that would change but no luck. The other weird thing is that even though it says my info is incorrect, it still send my phone number the two factor authentication code as if the sign in went through normally. However because I can't get past this screen bellow, there is no where to put in the code. Signing in through the Itunes app renders the exact same problem.

In addition to resetting my password like I said above, I've also tried to use the "Create Apple ID" button and still to after making a second Apple ID I get the same issue. Another random thing I tried was from the web dashboard for my Apple ID I tried making an app specific password but I couldn't sign into the app store using it either.

Alternatively I have tried to sign in directly in system preferences under the "Icloud" and "internet accounts" sections. Unlike when trying with the app store or itunes, this way accepts my password and Apple ID as correct, but I get a prompt to "enter verification code sent to your other device". Well, I have no devices attached to my Apple ID because I currently don't own any apple devices (my phone is an android - I know....buying a new laptop and iPhone are definitely on my list when I can afford it).

When I use this method, no two factor authentication code is sent to my phone or email, and like I said earlier, there is no "trusted devices" for me use to verify. Actually, I have never had a device registered with my Apple IDs. And obviously using one of the two factor codes that was sent to my phone via sms or my email that I received when trying to log in before don't work either (I new it was a long shot but I tried that too!).

Can anyone help me? Because while I save up for a new computer I still really want to be able to get the most out this device. Like I said before, I can't use the app store, itunes, use most browsers (and the ones I can I have to use deprecated versions with limited functionality and support), install third party apps or any sort of updates, or really do anything except use chrome (and even then I can't visit some websites because of the certificate issue).

It is totally impacting my ability to do work, as most of it involves working from home and again, this is my only computer right now. Sorry for such the long and possibly repetitive post, I just want to be as detailed in my explanation as possible in hopes that if someone can help, they have a full understanding of what is going on.

Thank you in advance for all your help