By “to master”, I mean “to have as wide a range of knowledge of vocabulary and idioms as a native speaker has”
Or is it possible for a non-native English speaker to surpass a native’s the knowledge of vocabulary and have a better ability to use it, by living outside English speaking country?
Some possible suggestions from a native English speaker:
Well, I would strongly suspect that living IN an English speaking country (as opposed to not living in one) and needing to use the language on a day-to-day basis will improve your ability to use it and maintain skills that already have. There’s a lot of nuance in the language (in any language, for that matter) that isn’t necessarily obvious from the textbook.
Another way to enhance your knowledge in terms of vocabulary and idioms is to travel to different English speaking areas and spend a non-trivial amount of time living there. For example, if you have been studying English in Australia, is there any way you could spend some time in the US? There are differences in language that are eye-opening even for a native speaker.
So much choice of vocabulary depends on context that it’s unlikely anyone could master the nuances of a language without using it regularly.
For example, the English word “run” has more than 90 definitions as a verb, noun and adjective, and also is part of several idiomatic expressions. The presence of a definite article (“the”) can determine whether a speaker is saying “I have holes in my stocking (runs)” or “I have diarrhea (the runs.)”
I used to teach conversational English in Japan, and yes, I’d say the English language is difficult for non-natives to master. Really any language is difficult to master after childhood, although just how difficult it is varies a lot depending on the individual’s ability and educational opportunities as well as how similar the language they’re studying is to their native language or already-mastered second language.
I don’t know that it’s completely impossible, but I think it’s extremely unlikely unless the non-native speaker is immersed in a community of native English speakers within his/her country.
If you were just asking about having a large vocabulary then I’d say a studious non-native speaker could probably learn the definitions of more English words than the average native speaker, but this isn’t the same as being able to use them naturally and in the appropriate context. Mastering the use of idioms might be even more difficult.
English is not my native language and until I moved to Canada three years ago, I had never lived in an English speaking country. Still, unless I tell people this, they assume I am from the US or Canada, and this was true even before I moved to Canada. People can’t tell from the way I speak English that it is not my native language. As for vocabulary, I would hazard that today my vocabulary is larger than that of at least some adults for whom English is a native language, if you just counted words. This was true some years ago as well; FWIW, before I moved I took the GRE and ended up somewhere around the 90th percentile for the language part of the test.
Here’s the thing, though: those are GRE words. Lots of people don’t know and don’t use them, but here’s a section of vocabulary that I’m good at, because of the things I read and the other languages I know, like French and Latin. More ‘operational’ or ‘cultural’ vocabulary, I never mastered at all. This is not about nuance in idiom or anything, I can handle that just fine. It’s things like ‘name three brands of laundry detergent’, or ‘name five clothing stores’. So that’s not really traditionally seen as being a part of mastering a language, and perhaps someone from let’s say the UK would face the same issue, but it is part of speaking and understanding the language and the things that people say.
For most, yes. There are people who have an aptitude for learning languages, and these people make it look easy (I correspond with a woman who has never left Argentina, but whose grasp of English grammar, usage, and style surpass that of most native English speakers in America. She has made a living from this. Certainly on this board there are many people writing in English as a second language who never give themselves away by their use of English, though they do sometimes stumble on cultural artifacts like slang or television.
The is more to mastering it than speaking – there is also reading and writing. I have been told by people who study languages that English is considered more difficult than many (Spanish, for example) because it is so irregular. For every rule of spelling, there are dozens of exceptions. For every rule of grammar it seems that there is some obscure context within which the rule doesn’t apply.
The “good” news about this is that a large portion of the population (I’m talking about America now, I can’t say what the situation might be elsewhere) borders on functional illiteracy already. Our standards just aren’t that high. 
All languages are difficult to learn for adults because we lose the ability to assimilate a language as soon as we hit puberty, but what also makes a difference is your native language. If you speak a Romance language, it will be much easier to learn another Romance language than English would.
If you speak Spanish, English is difficult grammatically but not impossible. It is much more difficult, and perhaps impossible, to match a native speaker phonetically, though, again because the neuro-motor (brain-mouth muscles) synchronization is much more difficult to achieve to perfection as there are many more different single sounds in English than in Spanish, and very few Spanish sounds are the same as in English. This makes it easier for English speakers to master the sounds in Spanish, but they will find Spanish grammar much more difficult to assimilate because it has no connection with that of English, which is much simpler.
I know whereof I speak. My native language is Spanish and started learning English when I was 25. My girlfriend says I don’t have an accent anymore, but I put in a lot of time in trying to learn. The long and short of learning a new language is that there are no shortcuts.
My first job in the US was as receptionist in a summer camp. There were areas in my knowledge of English and of American culture that were sorely lacking, but many others in which I surpassed the knowledge of many of the camp’s workers. My grammar and spelling were definitely better than those of every other person in the camp except two (yay me); some of my pronunciations got mocked… but the Brits happened to pronounce those words the same way and to also get mocked for it, so the problem there was not our pronunciation, it was the mockers’ ignorance of their own language’s variations and their lack of manners.
Is it possible? Yes. Is it likely, or easy? No, and you also need to define your terms better. Many native speakers (of any language) are familiar with a relatively narrow amount and variety of idioms; most people will have a much wider vocabulary regarding their interests than regarding things we don’t care about. In English, my chemistry vocabulary is much better than my sewing vocabulary, but - the same happens in Spanish! It’s not linked to language skills, it’s linked to personal interests.
Language is a means of communication and therefore, the answer depends upon the particular situation in which humans use language to communicate.
For instance: English is the predominant language in nearly all fields of science. So you could have a nuclear physicist from Mongolia who publishes highly sophisticated articles in his special field of research and he writes these articles in English.
However, this academician’s spoken English may sound really clumsy compared to that of a bright, 9 year old schoolgirl from Chicago.
In general, the Internet has made it much more easy for students of a foreign language to achieve a good level of proficiency without having much contact to native speakers.
The North Koreans used to abduct Japanese citizens to North Korea in order to have them teach and speak to North Koreans who were trained to be spies in Japan.
My favorite example of this is the word “shit.” “The shit” is different from “a shit” is different from “shit.”
In my experience with foreign learners, it seems that English is pretty easy to learn to speak at a basic functional level, but the devil’s in the details. Once you get into the nuances and bizarre orthography, it’s a bit trickier. That said, I’ve met many foreigners who speak perfect or near-perfect English (minus an accent) despite never living or only spending a year or two in an English-speaking country. I don’t get the impression that it is a particularly difficult language for a non-native to learn.
When a Spanish footballer and a German footballer yell at each other, what language do they do it in?
I suggest the OP do a search. This topic had been done here at least half a dozen times.