So I had a similar issue today, my pit stop showed all greens to count it, and I took it in the pit window and everything, but when I was leaving the pits and was past the speed limit and disabled my limiter, I started getting the warning and I still had the pit window up. I got the window closed and it didn't show that I had any pit stops remaining to do when I looked at the leaderboard in the MFD, but I was DQ'd at the end of the race. I read some other stuff online saying that you needed to close the MFD before the stop ends sometimes for the pit stop to "count", and so I tried the race again and did that and it seemed to be resolved. I didn't do anything differently otherwise.
I think it's still a bug, but potentially closing the MFD before the stop ends is a workaround.
As far as the speed warning showing up when you're not in the limit zone in the pit entrance, that's just a heads up that you're approaching the limit zone and need to get to the correct speed ahead of time - you can ignore it as long as you're at the limit before the zone starts. You don't need to engage the limiter just to make it go away.
If you're getting it on the pit exit, you most likely didn't have your stop count properly.
Or such is how it seems to me.