Surprisingly it does, and it really goes beyond that range. It won't show the over-the-limit FOV in the in-game settings, though. For example, 0.4 will be shown as 0.5, but if you start a racing session, it will use the 0.4 value.
I don't have much to say about that. I only have an FPS counter shown on the screen and in most cases it's enough for me, so I didn't bother looking for better options. If you don't have an FPS counter, you can easily use the one that's built in on Steam. Go to Steam -> Settings -> In-Game, look for "In-game FPS counter" option and select in which corner it should be shown. These are one of the most annoying issues, because usually they are caused by some factors that are outside of the game - other programs that are run at the same time or even system processes. It's hard to pinpoint which one causes it because there are so many of them; and other people can only give some general advice because everyone's system is different. Try closing other programs that you don't need to play the game (including browsers) and see if something changes... Yes, it's exactly that.