Paying it forward

I would like to precise 2 idioms in the text: 'difficult to stomack (=not so easy to cope?) and ‘in the nutshell’ (=in generally? ion main features? in the background?)

You’re right on both
‘difficult to stomach’ is the same as ‘difficult to take’ -also a common idiom meaning something, maybe bad news, is difficult to accept, handle, or cope with.

In a nutshell is a brief summary - as much information about the topic that you could fit inside the shell of a nut i.e. not very much, only the most important things

Yes - the phrase “difficult to stomach” can indeed mean that it is hard to take news and information etc, however it can also mean that you find it hard to believe information, similarly to “difficult to swallow.”

In a nutshell, as identified above, means the bare essentials of a point - only mentioning the relevant parts which are completely necessary to know.