How to embed python interpreter in UE4 via C++?

It’s 100% possible, engine is writen in C++ and you modules are part of the engine, so you can implement anything you can implement using C++. So quastion how to implment Python scripting and other quastions you asked is same as asking how to implement Python scripting in any C++ application and if it good. Here you have instruction how to add external libraries in to UE4

I think best way to implement any scripting language in UE4, is by pluging it to reflection system so you don’t need to bind invidual functions manually and have everything (except K2Nodes) that blueprint.has and more actully as there reflected functions but they are not blueprint binded. You probably will need to do type conversions and such too from python string to FString and such. There is ScriptPlugin, i don’t know it current status but it’s implementing Lua also using reflection system, so that might be good starting point for you (ofcorse it copyrighted by Epic so don’t copy paste it too much):

https://github.com/EpicGames/UnrealEngine/tree/release/Engine/Plugins/ScriptPlugin