hermetic study and psionic gift will not work with the slivers "poisonous 1". They will work with the cobra and viper though. I would decide on what you really want, slivers, or simply poisonous creatures and go from there.
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The longbow wont help with the assassin or sliver, and will negate your snake cult initiation if you happen to draw one. I would focus on dealing direct damage, or change your poison creatures to those that read "when ____ deals damage".
You are incorrect. Since damage is dealt during each step, a counter would be applied each step as well. The sliver with poisonous 1 reads "Whenever a sliver deals combat damage to a player, that player gets a poison counter." Double strike essentially creates two damage steps, and damage incurred during is "combat damage" both times, resulting in two counters.
unlike many other poison decks you actually have a plan for defense. Poison isn't fast. The biggest issues I see with your deck is a lack of reliably getting your poison creatures through on the attack, and not all that much poison overall. I would weed out some of the non poisonous creatures you have and add more poisonous in.
It would be an amazing deck if doubling season did anything for poison counters, but it doesn't. Your opponent gets the counters, and your opponent isn't a permanent you control. The Viridian Longbow wont help your slivers either, since they would need to do combat damage to land a poison counter. "Combat damage" only occurs when your creatures actually attack. You only have 8 creatures and the two serpent generators that could end up giving your opponent poison counters. Including the possibility of having other slivers out with poisonous 1, that's still not enough. If you really want to focus on poison you just plain need more poison counter creatures. I would suggest adding black not only for pit scorpion or swamp mosquito, but for snake cult initiation. If you enchanted a marsh viper you'd deliver 5 poison counters in 1 shot. If you're dead set on increasing poison counters through other means, there are two routes to take; You can turn poison creatures into timmies and land poison without attacking, or you can increase your attacks to land more even more poison per turn. If you go with option one, keep in mind the only creatures that are useful are those that read "If ____ damages a player". The others need to do combat damage so they have to attack (or attack and not be blocked). The perfect combo is Viridian Longbow with marsh viper and a method to untap like instill energy or even better freed from the real. If using blue hermetic study or psionic gift also work instead of the longbow. If you could set up the perfect hand, this would be a more mana effecient way to win. Option two is somewhat more straightforward, but can still have tricks up it's sleeve like fireshrieker. Perfect combo would be Marsh Viper with snake cult initiation and fireshrieker. Win in 1 attack. You have more flexibility with this build in that you don't need to rely on specialized combos to execute the strategy. If using red, firewhip also allows a timmy effect, and relentless assault and pandamonium are excellent additions. adding trample to get damage on the player is always good, as are cards that make creature unblockable (shadow is also good, flying, and sometimes even landwalk). Poison isn't the easiest way to win, but it is fun!