Hard drive sometimes found - sometimes not

That's good that the drive's working now! You could check it's health again now, just in case.
About that ~8 MB Unallocated space.
There could be two options in which up to 7.8 MB of Unallocated space, that's not manually set up, can be detected on a hard drive. The first reason is when the Unallocated space is at the end of the disk, but this is not the case.
Your 7.8 MB of unallocated space resides at the beginning of your hard disk. Normally this means that there are no Primary partitions on the hard drive and the hard drive contains only an Extended partition. In such cases Windows reserves the minimal amount needed for creating a partition (7.8 MB) in order to be able to handle the only Extended partition properly. It isn't recommended to remove this area. Even though technically it is possible to merge it with the Extended partition, this may result in the data on it becoming inaccessible.
Disk Management can't pick up on that Unallocated space, but some other software can.
So you shouldn't be worried. :)

Cheers!

CK_WD

Good news on the small partition.

On the health aspect, I ran a CHKDSK and received this error;
The second NTFS boot sector is unwriteable

Next question: why does my C: drive always appear last in diskmgmt - and as disk 3 of 3 - when it is set in the bios to be first?

The CHKDSK error means that bad sectors have been detected on your drive. You could fix it with the chkdsk command: chkdsk X: /f, where X: is the letter of your drive. This would fix any errors on the drive, but once bad sectors occur they quickly multiply and fixes are only temporary.
Another option is to use the WD Data Lifeguard diagnostics tool to close the bad sectors:
Support Answers

About your drive C, sometimes, disk drive numbers may not be the same as the SATA channel numbers. There is no direct relationship between the BIOS order, and the order in which Windows numbers the disks. Your C drive is set in BIOS to boot first, as that's where the OS is. The disk numbers that are assigned by Windows are dependent solely on the order in which the disks are enumerated and processed by Plug and Play. Meaning that in most cases the first drive plugged in from the beginning, becomes Drive 0. This article from the Microsoft support page may also help:
https://support.microsoft.com/kb/937251

Cheers!

CK_WD

WD Data Lifeguard repaired the errors. Fingers crossed it holds up. Thanks!

Hey, I'm glad the errors are repaired, you're welcome! :)
Just remember to keep regular back ups! If you don't have enough (different) hard disk space, then you could always use an online Cloud service.

Cheers and good luck!

CK_WD