What kind of glue should I use to glue sea shells to steel and sea shells to stone? These will be displayed outside. I have tried a hot glue gun but it doesn't do well outside.
Depending on how ‘shock-proof’ you need it to be, you have a couple options: silicon or epoxy.
Silicon is a bit more flexible, so if people or pets are going to be touching it, then this is what I would recommend. It is waterproof and really sticky until it dries. My advice is to get the transparent type used in bathrooms.
Two-part epoxy is theoretically stronger, but it might actually be too strong and might not bond well-enough with the steel.
Whatever glue you use on steel, the preparation is extremely important to maximize the bond strength. The science behind it has to do with surface energy and other cool phenomena, but the gist of it is if you scrub the metal with Comet (yes, the old-school powdered bathroom cleanser) you'll get the best possible bond.
The test for whether you've succeeded in activating the surface is to place a drop of water on it. If it beads up, you've got more work to do. If it spreads out, you're ready to go. Don't touch the surface after scrubbing it. Just rinse it thoroughly and leave it to dry or hot air dry it if you want.
If you do this before epoxy, the bond will be all but unbreakable. There are other acrylic adhesives that will also bond well to metal, and polyurethane glues etc. There are a lot of other considerations like visual appearance, flexibility, having-some-around-already, etc. that can narrow your choices, but proper preparation will make a lot of things work that wouldn't work at all otherwise. I bet you'd get surprising performance from white glue (Elmers) with good preparation.
I couldn't say about the stone, from personal experience anyway, but I expect a good scrub with Comet will go a long way with that substrate as well. The conventional wisdom of using solvents to clean with might improve the surface, but will always leave behind a micro-layer of hydrocarbons (oils) that interfere with bonding. These contaminants get on everything exposed to air, so you don't have to necessarily handle the item to contaminate it.
Sunlight (UV rays) will degrade many adhesives over time, so that's another thing to consider. I expect most epoxies would hold up a long time on that count, although of course they're not the most convenient to use.