I'm just going to talk about 5. Because I'm feeling to lazy to analyze all of these.
I like the LeeSin pick to apply early pressure to top to ensure that Vlad can either get ahead, or survive till late game.
The super fat wombo combo with Leona, Galio, and Vlad is HUGE with good initiate on it, but also a good counter initiate.
I would be willing to substitute Sona or Taric just for what is in my opinion a stronger lane. ESPECIALLY if Taric is considered a counter.
Could switch out Galio with Orianna, since you put the ball on Lee or Leo and get relatively same effect as Galio Ult. Once again for a safer lane.
Would go with Ez in this comp just because his Ult stacks well with Vlad ult, and he has strong ability to kite, with a team that somewhat relies on using damage for peel. But I'm a firm believer that FotM Ad's fit in with anything. So graves, cork, ez. All good choices.
I will say for the most part your counter lists are very short, because really, its not champions that beat comps, its a theme, or a certain comp. For instance, a team with Skarner, Gragas, Sona/Taric, any AD, and an Irelia or something. Would do really well against this team.
-Skarner is fast enough in jungle and has good enough early game to wade through the LeeSin pressure, Irelia, Grag, both safe lanes with good mobility. And Skarner scales better than Lee off of utility alone.
-Gragas ult says **** you with disengage.
-Your proposed team is looking for a perfect fight, and my proposed team can pick when they want to fight pretty handily with Grag, Sona, and Skarner. Can Disengage with Grag and Sona, can Engage with Grag, Sona, Skarner, and if at any time you want to initiate you HAVE to catch all 3 of them in Your mid ulti to get full effect.
So I'd add themes, that counter your teams instead of champs. So for Team 5. It would be, Hard Engage, Hard Disengage. Team-Splitting Abilties (i.e Grag ult)