Hi, yes you can. I would suggest you use E6000 or Wellbond to glue the glass pieces down. They're both UV resistant and waterproof. To grout use an outdoor grout. Your local hardware will be able to give you advice of which is the best to use in your area.
You're most welcome. Have fun with your project
Unsanded grout to fill the gaps between the glass. Seal the grout with grout sealer
Hi. Will the orbs fit inside of the glass? Are you able to provide a picture and we will definitely see what can offer as help.
Here's some helpful information: https://blog.mosaicartsupply.com/mosaic-gazing-spheres/
They note that you need to seal the orb after you finish it, "seal the mosaic with a tile and grout sealer, which are invisible pore sealers that wipe on and wipe off. They aren’t coatings that form a clear layer over the surface. We use TileLab brand that we buy at Home Depot."
Hi DK: You might be able to coat them with Polyurethane. It's a synthetic resin and type of varnish used in the finishing of floors, cabinets and other woodwork. It is a desirable choice of varnish because it is transparent, water-, fungus- and mildew- resistant, and resists abrasions. Good lluck
Have you considered a marine varnish? It will hold up under weather.
Hi! Found this and thought it might help:
Treat them like mosaic tiles and use Ceramic Tile adhesive and grout waterproof .