Contact Milkman for the ins and outs of acrylic tank builds. I think he has his 350g in the sticky section.
As for using 1/2 inch for the bottom, I am certain you will be fine. There are many 1/2" acrylic tanks out there that are 24" tall. The main reason for having a thicker bottom is for gluing surface at the joints. You can cut 1/2 x 1/2 "rods" to line the bottom joints. That will give your bottom an area of an inch wide for the sides to grip onto.
As for using 1/2 inch for the bottom, I am certain you will be fine. There are many 1/2" acrylic tanks out there that are 24" tall. The main reason for having a thicker bottom is for gluing surface at the joints. You can cut 1/2 x 1/2 "rods" to line the bottom joints. That will give your bottom an area of an inch wide for the sides to grip onto.