1) I've got an NTFS data partition that my Windows and Mint partitions both use. When Windows sees that Mint's been changing it it sometimes tries to "repair" the partition, resulting in all of my version-controlled files saying they've been changed. How do I stop this? For reference, the data partition is after the Mint partition, which is after the Windows one.
Easy. Mouse the partition with the "ro" option.
(I would not trust NTFS as a cross-platform partition type, at all -- its internals are not as publicly documented as most other filesystems, and that's by design; if you are using it in this way, I strongly recommend that you backup the entire partition regularly)
2) Ctrl-F doesn't work in Mint. In any program. The keypress just isn't detected. If I use xbindkeys it shows that when holding control, pressing F doesn't even register. What up?
I take it that it shows both buttons being pressed when you run xev, right?
(warning: seemingly pretentious underlined section headers follow; I put them in because my response was getting a bit walloftexty, so I thought it'd be easier to get the gist this way)
First, you want to see if the combo works at all
Try switching to a vtty (hit ctrl-alt-f1 and hope to the gods that your distro didn't disable this option, as it's genuinely useful) and see if it functions there (in terminals, ctrl-b acts like the left arrow key and ctrl-f acts like the right arrow key, so you can just type a bunch of text, hit left a few times, then try ctrl-f to see if it moves the cursor to the right).
Then, you might want to try a different desktop to see if your specific desktop is the problem
My first guess would be that the above two items works like a charm and that the desktop environment you're running accidentally reserved that key combo as a keyboard shortcut. Try logging into a different environment or window manager to test it. LXDE is a decent quickie one to try (I think the package in your distro is "lxde-core").
Check to see if your keyboard shortcut is being intercepted by your desktop
Anyway, I'm guessing that Mint uses Gnome 3 as its default desktop and that you are using that. Despite using it for the last week, I can't remember exactly how you get to the shortcuts. It's probably something like "right click on desktop, click "Settings", click "Keyboard and Mouse", choose "shortcuts" tab). I don't think it had a filter bar, which would be really really nice right now, but you can scroll down every line to look for an errant ctrl-f that it might have added. If it's binded at the desktop environment level for some trivial action, then regular apps might not see it when you hit it.
Also yell at me if all the above seems stupidly complicated.