Hey, I'll attempt to answer your questions.
1. Programming can be quite difficult, getting into, but after many weeks of dedication, commitment and frustration, you will quickly start to speedup.
2. You will do some math when programming, though most of your thoughts will be about how you can achieve a certain goal by combining the "tools" you have at your disposal.
3. When programming for Cryengine you have to use the language C++ and Visual Studio will be a very good choice as your IDE. There are also some plugins like CryMono which allows you to program using C#. You can also script using Lua.
I hope this was of some help, though I'm not the programmer on the team