Your post is a bit unclear. First is easiest: if you expected to be paid for the time off and ran out of sick leave, you'd expect the employer to charge your vacation time. But it's not precisely clear that you took time off as such if you were still doing all your work.
While an employer's free to accommodate intermittent FMLA, you aren't saying what it is you presented with them as needing. You mention working from home, but that doesn't tell us anything. I suppose this employer wants to be able to keep track of how much FMLA time you're actually taking off, but as a practical matter, it doesn't seem like you're taking any. If you are exempt and you're getting your work done, however, and there's no definite "off" time, I'd say the employer is playing fast and loose here. With an exempt worker who keeps working, the "part time" thing as to intermittent FMLA might be hard to navigate.
I suggest that you talk with the nearest federal DOL wage-hour division office, or the main body DOL in DC (or even a local employment law attorney who deals with FMLA violation-related cases).