Hi Ginger,
If you want to have an equal front and back half, then you will need to cast two of each piece and glue them together. You can either glue together with some unmixed resin, or you can use E6000 — https://shop.resinobsession.com/products/e-6000-epoxy-jewelry-adhesive
Alternatively, if all you want is just a little bit of a dome so it doesn’t look flat on the back, you can try the technique in this video on our youtube channel — https://www.youtube.com/watch?v=DkZdO1n9R7QOnce your resin is fully cured, yes, you can drill, carve or sand it as necessary. We have several videos on those techniques on our youtube channel as well:
https://www.youtube.com/watch?v=M7Ippav162g
https://www.youtube.com/watch?v=fWii42EtJkM
You can easily get the frosted sea glass appearance to your resin by using a very fine grit (1000 or higher) wet/dry sandpaper.
Good luck!