Gina, we removed shower doors and just went with a curtain. I've been planning to mosaic them to help shield a big electric box in our yard. I think GE Silicone2 would be best because it can flex with weather changes.
I'm sure you can grout if you want. I hate grouting, so I've started just butting all the glass or tiles as close as I can get them. It looks fine, is quicker, and isn't as distracting as grout lines. I have a tile saw, a glass saw, and a glass grinder. The grinder is used the most to help shape pieces. You can often find them in the thrift shop. Just be sure to wear a mask when grinding. You don't want that silicon dust in your lungs!
I need to get going on that project. I'll post pics when I get done. Please post your pics too, Gina! I'm going to attempt a greenhouse look with lots of plants and flowers.