Yes, I have had the buttons disappearing few times to me and I can confirm (based on my experience) that this is due to lost connection/poor bandwidth issue.
To confirm, a couple of times this happened I had received mobile message “No Internet” or wifi strength being poor and mobile trying to switch between wifi/mobile data. Further, if the Internet connection comes back, the buttons do re-appear and I was able to continue the matches.
As for the opponents being faster than they should, there are now dinosaurs with Insta charge, bellow, cloak, other moves that allow them act first even if their speed is slower.
Then, when you use Thagomizer/superiority strike or other speed decreasing moves, I have seen the app initially showing speed comparison incorrectly but switching to correct speed when you perform the action.
Also, I think if you swap-out a dinosaur affected by a speed reduction move (e.g.: Velociraptor affected by Thagomizer) and then want to swap-in back during future moves, the system shows it as slower. I have not confirmed if the speed is actually still reduced or it is just a visual glitch.