Splitting up huge curved faces in Blender gives strange behavior

Recently I have been trying to make a world map, on a 3D sphere, with meshes, split up into various countries which you will be able to play as. And I want to split those countries into provinces. The problem is my countries are basically just huge faces with a lot of vertices in them, and countries like Russia run into this problem where when I try to split them up using the knife tool it just goes crazy.

In the 2nd picture the vertices at the border of the split seem to literally just go down for some reason. I think it has to do something with how huge these faces are

Oh yeah also if you look at these huge countries from the side (without even splitting them up) they seem to glitch out and make these weird shapes.

I think it’s because Blender doesn’t know how to really handle these huge single face objects.

Would you mind showing the wireframe?

Yeah sure

Your vertices don’t have any connections. Press CTRL + T to triangulate.

Am not sure what vertices having no connections mean, but I’ve tried this and I think my original problem is solved. The thing is that it’s now kinda bumpy.

By no connections I mean the faces don’t have any topology. Without face topology your mesh is practically in the form of an impossible shape. You should’ve started with topology from the start. What I would recommend as a fix, is to use a modifier to increase the number of vertices, and then apply a cast modifier to make the it round.