How many vertices can I connect to a face? I was wondering how many vertices I can connect to a face. I mean, when modeling, I can connect as many as I want, but is it allowed to do such stuff? 



Because I know that if I raise a single point on one of the edges on the example below, the face will have a strange form. 



If you look at that from different angles, you can clearly see that there are edges but that aren't selectable (I don't know how to explain that). You can see them but there's not an outline of them.

So my question is, if I don't have the intention to move the surrounding edges of that big face, can I leave it like that (image  1)? Or do I have to triangulate it or what?

Ps: Maybe for a basic scene it doesn't matter. But I do it for a game that's why I'm wondering if I'm doing anything wrong.

Thanks
If it's a big flat surface, it is absolutely fine to leave it as Ngons. A polygons with more than 4 vertices are called N-gons. For rendering and UV unwrapping there should not be much issue, if it's going to be staying within the blender environment.

However if you are working on models that would be exported into a game engine, it's best to define your 4 sided polys all over your meshes as much as possible. Games engine tends to mess up your triangles when no definition of edges are found. They pretty much auto tesselate your meshes for you, which usually produce "unhappy" results producing in-game artifacts.

The link that iKris posted is pretty clear on a number of reason when to use them, and when to avoid them.