I have trouble with things like synonyms so I try to make use of a thersaurus. I've not considered the strenght of words. That seems inspiring. I also think non native speakers can actually become advantaged when it comes to testing on English. I'm told a lot of natives don't touch the basics for a while so it seems I did better than a lot in the standardized testing of English simply because it is fresh in my mind. If you hear me speak though my minor accent betrays that I wasn't born here. That said, I struggle with idioms and colloquial expressions. I remember being confused with "pulling your leg". Living in the South East for a time, there is a lot of idioms and expressions. Seems like most of what southerners say is idioms that make no sense to non native speakers and probably even Northerners. I also think it helps that US movies are so prolific and immitation goes a long ways. Just don't trust the depictions of southerners. The sound is way off and over dumbified. Also, I started watching a lot of UK tv shows. It seems to help me since they seem to have a wider use of vocabulary. They also seem to have less idioms.
Yes, this is where English gets really hard (or any language for that matter). It takes a great deal of self-awareness and personal humility to master a language, because often we have to make mistakes on our own. In our first language, we have the luxury of being children and of being surrounded by people who will guide us to speaking that language "properly". As adults, we are expected to be much more capable and fairly or unfairly, that puts adult language learners in an awkward position. All of that said, the more you engage with native speakers, the more you can start to notice patterns and connections. You absolutely did the right thing by letting people know that English isn't your first language. In my classes, I absolutely encourage students to engage in discourse and argument, but also to qualify their statements with things like, "In Spanish, this word has a negative connotation and that's not what I mean to express, but I don't have the language to say exactly what I want to, in English. The idea is like . . . " and again, that takes a lot of humility and strength to do. Anyway, you express yourself pretty well. I agree whole-heartedly that native speakers do not know as much about grammar as English language learners do. At the end of the day though, language is one facet of good communication skills. Establishing rapport and engaging with others is really what the site is all about.