Physics engine in AssaultCube (ragdoll)

[tempest]

How exactly are the animations done, for running and such? Is it just a series of models being shown one at a time then?

Yup, that's basically how MD2 and MD3 work. MD5 however uses skeletal animation, which means that the animation just describes how the so-called bones move, and the engine uses that data (and the vertex weight) to move the vertices (i.e. animate the actual model).