What devices can I use with a mini tripod?

Most mini tripods offer the ability to attach your camera or smartphone possibly even your tablet computer. Most consumer cameras are fitted with a standard 1/4-20 UNC thread that attaches to the tripod base. A smartphone can be secured with a special holder that, in turn, attaches to the base. Check what features each tripod offers, as they vary. Some will offer one attachment or the other while some will offer both.

How stable are these tripods?

They're very stable, but there are a couple things to watch for. Some mini tripods have bendable legs that adjust or even wrap around objects. Whether the legs are adjustable or not, once you have your device mounted on the tripod's base, be sure it is stable, or it might tip over, especially if the legs are too close together. Set a solid foundation by adjusting the legs to a suitable distance from one another. If you're setting it on solid ground, be sure the terrain is relatively flat or adjust the legs to fit the terrain.

What are the advantages of a mini tripod over a "regular" tripod?

Portability is the biggest advantage. Many mini tripods fold down so they can be placed into a backpack or bag easily. Many of them are also flexible, which allows for creative mounting on a fence, tree branch or almost anywhere.