I've read (and vaguely understand) that NTFS drives cannot be filled up past 85%- if they do, bad things happen.
Your understanding is close, but not quite right. You can fill a drive all the way up, and it does not matter what file system is used to format it. Whether filling to the max will cause problems or not, depends on how (where) that drive is used. For example, assume two identical drives, one the boot drive as C drive, the other as a secondary drive D. C drive contains a default installation of Windows, and is where you install all your applications, such as Office, anti-malware, or your games. D drive is for storage and backups.
You can stuff photos, songs, and document files into every sector and byte of your D drive and not have any problems. This is because the files just sit there, and rarely change - therefore there is little "drive activity" going on. Reads maybe, but not many writes. Reads don't force a change to the MFT, writes do.
But if you fill up C drive, the boot drive, you will be dead in the water in no time, if not sooner. The operating system needs a certain amount of free disk space to work in. When Windows starts, it opens many files and creates a bunch of new temporary files. It needs free space to do this. Like the OS, many of your programs expand when opened, not only into RAM, but into temporary files too. This is one reason power failures and sudden shutdowns are bad - files are not properly closed, and temp files are not purged as they would be with a "graceful" logoff and power down.
The Page File expands and contracts as needed - even if you have lots of RAM (remember - I'm talking default settings). Your Internet browser creates lots of temporary files and cookies. With lots of free disk space, you may have files scattered all over, but they tend to be less or not fragmented at all. When space is low, fragmentation becomes an issue. When disk space is very low, System Restore gives up all it has reserved, as does the MFT give up what's left of what it had reserved. When there's no room for temp files, page file expansion, or changes to the MFT, the system crashes.
Why does the MFT need so much space?
Because it has to keep track of every file and it's attributes on the disk. And that can be many 10s of thousands of files. The space needed by the MFT will grow and contract depending on the number and size of the files stored.
if the MFT becomes fragmented, major problems happen
No. That's not right. When the drive is first partitioned, the MFT snags 12 percent of the disk for itself (this is still shown as free space, but it belongs to the MFT). If the drive fills up and a file needs more space, the MFT will give up what it is not using. Then, if the MFT needs more space, it will fragment itself and run just fine. A fragmented MFT may slightly affect performance - but it is more likely if the drive is that full, the system is choking already due to lack of free space.
Does the 85% rule apply to the whole drive, or the partitions as well?
To the boot partition it does. Or if like me, you moved your page file and changed all your defaults to a second drive (or partition), or you install major applications on the other drives or partitions. By major, I mean like MS Office or your full time security programs - programs that use lots of resources (RAM and CPU horsepower), or programs that have frequent updates and changes.
That said, keeping 15% free disk space on the secondary drives is probably safe, but if you are pushing less than 30% free space on your boot drive, and you keep using more and more space, it is probably time to move some stuff off that drive, or replace the drive with something bigger. And truthfully, it comes down to gigabytes, not percent. 150Gb free on a 1Tb drive is plenty of free space. But 4.5Gb free on a 30Gb partition is pushing it - especially if the disk is fragmented too.