Twitch's laning phase is one of the weaker of the adc champions. No, you cannot straight up trade with an opponent adc like with others (for example Ashe, Lucian, or even Ez with his range) at the early levels. Even when you do hit level 4, if you dont have enough AS, trading can still be a challenge. And no, you don't need a poke mage to do well with Twitch in lane.
The key is to be patient and always moving. Be opportunistic with some AS from your rune page (either split glyphs between flat AS and MR or have pure AS) so you can get your combo off quicker when your opponent steps up to cs. Twitch is all about positioning, so it will just take time to get used to him.
As for supports, it helps to have someone with a stun, root, or grab. Leona, Blitz, Thresh, and Alistar (a good one) are what I think are the best synnergy for Twitch as they can apply pressure, tank, and peel without putting Twitch in a bad position. Taric is okay, but requires you to get close to someone or out of position to stun. Braum, Soraka, Nami, and Janna are also good, but take some getting used to to work with.