1. If you know or suspect that your opponent has higher initiative than you, just plan your fight around it. I used to fight this Lightning main that was faster than me, I knew he would always go before me on round 2, and his AOE paralysis would mess up my combo. So after the 4th time I've lost to him I decide to just let him go first on round 2. I let him do his fancy paralyze/acu chase on my main, but then I just use my healer to clear everything, and then use my main right after. Or you could just prepare beforehand by disabling their main mystery user before round 2 starts but after his healer acts, making it so he can't clear it in time.

2. There's a counter to passive barriers. It's called active barriers like Sasuke, Anko, Haku, Hashirama (lol). Most people will be using Sasuke but there's your simple solution. If they aren't running a round 1 disable then your barrier will go off and replace theirs. If they do disable your active barrier user then they won't have that skill available for round 2. If they still manage to beat you then you probably weren't gonna win in the first place.