The error messages you're getting there are to do with OpenGL.
That's a graphics API (OpenGL and DirectX are the two main graphics APIs), so there's an incompatibility with the way your computer is trying to render the emulation.

Probably the best chance of fixing this would be to try a DirectX plugin (Pete's Direct3D plugin is the best), or Lewpy's Glide plugin if you have an older graphics card. If you do, indeed, have an older card, you may want to try Pete's OpenGL1; OpenGL2 was made for newer ones.

The other thing you'll want to try is in the video plugin configurator in ePSXe, set it to "compatibility mode", to lower the settings down. This will ensure that the emulator isn't trying to display something beyond its capabilities.

As for the "resolution raping", that's normal - when you start a game, it can't be displayed at your monitor's native resolution, so it has to switch down sharply. It's supposed to return to normal after the game closes, but sometimes it will stay that way if there is an exception or error somewhere.