Keeping screen turned on for certain pages

You can't do this without platform specific services or renderers. A portable project will have to call platform specific code in order to achieve this.

From that platform specific code, either as a DependencyService or Renderer, you can access the Window object through the Forms.Context. The Forms.Context is your Android Activity, through which you can reach the Window object.

On Android it works like this:

Android.Views.Window window = (Forms.Context as Activity).Window;
window.SetFlags(WindowManagerFlags.KeepScreenOn);

On iOS you can try this (Apple docs):

UIApplication.SharedApplication.IdleTimerDisabled = true;