http://www.themanadrain.com/forums/viewtopic.php?t=20790&sid=82ceae80d280559b4bd3cef6070756d3This is basically the "what to include" thread, as well as having a bunch of decklists (including Andy Probasco's). I'll try my best to answer all your questions, as well, based on my T4 experiences. (I play with Andy's deck almost weekly and have a hand in creating/tuning it.)
1. Counterspells: We do not have nearly as many as most, despite having a lot of very big bombs, and it suits us just fine. For the most part, We only have the counters that do something at least marginally special, from Desertion down to Rewind. We don't include basic ones (Counterspell, Spellblast), or the political ones (Vex, Arcane Denial, Fold into AEther), though most people seem to include every counter available to them.
2. Again, we are light in this department, and we're okay with it. Basically, we never want to have a dead card in our hand, including answers. We have a handful of spot removal, all of which does something special as well (Agonizing Demise, Ray of Distortion). We generally don't include the basics (Terror, Disenchant), or the situational (Chastise, Death Stroke). We also run very little mass removal, limited I believe to just Obliterate, Red Decree, and Uktabi Kong. Again, we are in the minority in this depsrtment, as most others I have seen run nearly all printed mass removal.
3. I think that is the key reason why Andy's deck is so much different from everyone else's. Our core playgroup loves the combo aspect above all else, and it shows. If we're about to pull off something cool, we don't want it countered. This is a tough ratio to get down, but just like any other format, playing with the deck enough and weeding stuff out/putting stuff in after each play session will eventually result in a good deck. Or you could just netdeck one of the decks in the above link.
As for the specific cards:
Most people use Memnarch and Door to Nothingness. The Door isn't nearly as broken as one might think, as it can almost always be killed before it untaps, or Stifled afterwards. Memnarch is first-pick good, but you need some broken, right?
We've tried CotV and, while it's cute, it's bad. Void is almost strictly better, and that's bad too.
Firebreathers: Again, Andy's deck is one of the few that use them. We actually only use the best of the best (Kamahl, Fist of Krosa, Avarax, Cromat). I recommend starting small (Pygmy Pyrosaur is probably the worst, besides firebreathing Walls), and start working up and see how much the deck can handle.
Staff of Domination: Andy uses it, and probably no one else. THIS CARD IS STUPID. I do not recommend it, unless you put some sort of usage errata on it, which is something we stay away from.
Biorythym: Unless you have someone stupid in your playgroup that is likely to cast this on turn one for the draw, there isn't really a problem with it. We use it, and it's pretty average. You deck really has to be good with it, and it's hard to resolve, so it's usually a last/second-to-last pick.
Infinite amount of creatures: Even we don't use those cards. The only way for that to happen in our deck is Greater Morphling/Uktabi Kong.
Sorry for being so incredibly long winded, but once I start talking about Type4, I can't seem to shut up!