Do you have a jointer? Biscuits are not necessary. As long as you have straight, flat and clean joints, all you need is a good wood glue and clamps. Titebond II or Titebond III will do the trick. Yes, you can joint 1/2" wood on a jointer. You can also do it on a router table with shims. Look it up on YouTube.
If properly done, the glue joint will be stronger then the wood.
Will this be a stand up puzzle or a tray puzzle? If it is a stand up puzzle, 1/2" is not thick enough. You will need 3/4" or thicker.