Is there a way to create meshes at runtime?

I'm not exactly sure what you mean by "meshes" so I'll explain everything i'm assuming your referring to

You are not able to create/edit meshes in realtime on Roblox, they are imported objects you have to upload. You however can use Roblox CSG, aka unions. In the past few months Roblox has released different improvements and APIs to CSG to add a real-time CSG solver. Here is an example from the wiki of the real-time CSG system as well as this example, from the devforums, created by CloneTrooper1019. The current technology is not necessarily as fast as I personally think it should be but it is a very recent implementation to Roblox so you should be able to see improvements in the next coming months. Just in case you couldn't find any of the API's for it, I've linked them here.