I'm not seeing either of these bugs with the plugins I have access to. Turn order works as expected, both on the turns the multitechs are used and future turns. Perhaps there's an incompatibility with the two I don't have - Weapon Unleash or Status Menu Core? It's hard to say from here without more information.
When the skills activate, do the skill icons disappear from all involved actors? They should - and do when I test.
One other possibility is a change made to the base RPG Maker MV game code - who knows how old this test project is? - but I'm not expecting that to be a factor. EDIT: Nope, all is fine in a fresh project too.