For buffs, and some polymorph skills, that is a known issue that they can go on cooldown but not apply the effects, which should be fixed in the next update (no ETA yet). As a temporary workaround, saving and reloading should get the skills working again.
A character getting stuck with a disabled skillbar is also a fairly rare, known issue. Saving and reloading should also fix this. It was more a little more in the last update, but the main cause was fixed in the latest update.
If you run into this again, please save when it happens and email it/them (or a Dropbox or Google drive link, etc) to supportdos2@larian.com, with a brief description of which character was stuck and what was happening when it started (entering combat, etc).
Even better would be a save before it occurs, with a way (at least semi-reliably) to reproduce it, but so far nobody has reported a way to deliberately trigger this problem.
The programmer looking into this was not able to reproduce it in the latest game version, so at least having save(s) with information about the state of everything when the bug occurred could help in tracking down the cause.
Each save is a folder in the '..\Documents\Larian Studios\Divinity Original Sin 2\PlayerProfiles\<ProfileName>\Savegames' folder. In Windows Explorer you can zip a file or folder by right clicking on it/them and selecting 'Send To | Compressed (zipped) Folder'.
