No, you don't need to kick out your Thundrake to capture an Icedrake. You can have one of each type of monster (ie: one Thundrake, one Icedrake, etc...). You will get a second dragon soul, but there will be no problem with capturing the Icedrake, unless you already captured and Icedrake and haven't released it.
Monsters can be killed with the No Dmg to Animals rule by confusing enemies, and using counter moves, as stated above. Charm works well too, and isn't as hit or miss as confusion. But both charm and confusion will get you a yellow card, so counter moves are your best bet (other than not going in to battle with the No Dmg to Animals law in play).
Oh, and while Goblins do go extinct, a Blue Mage can learn the Goblin Punch at any time in the game. How? Simple, Goblins are one of the enemies that appear on the multiplayer maps. Find a friend, play a multiplayer game, take your Blue Mage into combat. Get him to learn Goblin Punch, and he should keep it once the battle is done. (I don't remember if this works on Thundrakes too, but Goblins go extinct much earlier, so hope this helps)