I'm curious about if there is any guarantee about the amount of angles that can be concave in a given polygon. I'm wondering if there's a relation between the number of convex/concave angles, and specifically if it is possible to have a larger or equal number of concave angles than convex ones.
Yes, it's possible. The simple example with the equal number of "convex" and "concave" angles could be the following: hexagon with the vertices (0,0), (7,0), (4,1), (2,2), (1,4), (0,7). And you can add an arbitrary number of "concave" angles, so an equality isn't a requirement.