Macbook can't find startup disk

I am a dope. I tried to erase and reformat the disk as it was inside my computer. Formatting it in an external case worked.

I first formatted it as APFS, reinserted it into my Macbook, booted in Recovery Mode and tried to reinstall OS X, but it was stuck at 'about a minute remaining' for over an hour. I looked in the log and there was an APFS error over and over again, so I shut down the Macbook, removed the SSD, reformatted it to Mac OS Extended (Journaled) and inserted it back into my Macbook and tried to install High Sierra again, was able to select 'Saidas hard drive' as the drive to install on--but this time , I received the message 'Permission denied.' After a few minutes, when I went into Disk Utility again, my drive was greyed out and appeared as 'not mounted.' I had ran Disk Utility before attempting installation and the drive WAS mounted and was not greyed out. What gives? Is this a case of a faulty SATA cable? What other troubleshooting can I do before ordering a new one?

The first two screenshots are of the drive in the external case connected to another computer; the next pictures are of the drive in my computer.

An update: I downloaded the Sierra installer onto a USB and connected the SSD to the computer through an external enclosure. I turned on the computer and (accidentally) forgot to press the command to go into Recovery Mode--and the laptop went and installed Sierra, no problem. I then tried to put the SSD back into the computer and boot, but the progress bar would get stuck on 100 percent. Took the SSD out, tried this electrical tape fix (MacBook Pro Hard Drive Cable Failure - Free fix and preventative maintenance - Question mark - YouTube) but it unfortunately didn't work for me. I've ordered a new SATA cable and will update if that does it.

Next: again connected the SSD through the external enclosure, was able to boot without a problem, and tried to update to High Sierra (this was, by the way, what started all the problems--I had downloaded it, the battery died, and when I plugged the computer in and tried to turn it on, I got the flashing question mark on the folder.) Now I got this:

Now reading forums and trying to find another fix for the missing firmware partition.

So, I've tried erasing and formatting it but received the message 'Unable to write to the last block of the device,' both in Disk Utility and Terminal. This all happened, by the way, after completing the last Sierra update in January and then the battery running out while the computer was still on but shut.

Erased the SSD again, formatted it as OS X Extended, ejected the USB case, then put it in computer (whenever I use the USB case, I plug it into another Macbook), and the properly formatted drive shows up again without a problem. It's only after having put it into my laptop that it was unmounted.

Now I've plugged the SSD into the external case again and 'Saidas hard drive' has disappeared and I have disk2s2, which is greyed out and not mounted.

Thanks for the reply! I will try reformatting it, but when I installed the SSD a year ago, I had formatted it.

It seems that formatting the SSD isn't a problem after all--because i can do that easily when plugged into an external case.

Sorry, that's going above my head now. What is that exactly?