This has likely been answered on the forum, but I my searches found nothing so here it goes - With the Alchemist brew potion feat, can the alchemist brew a third level potion at first level? It has to be one he knows, but he gets to pick 2 for free + int mod.
Brew Potion restricts the alchemist to using his class level for his caster level. So, 1st level alchemist only brews CL 1 potions.