mianders:
How many times should you check a new story for typos, better ways of saying things, better words or expressions, etc.
There is no 'should' when it comes to these things. You have to do it the way it works best for you. Personally, if I tweak too much I become perfectionist to the point of sabotaging myself, start hating the story and delete it. I definitely have to be careful to not overdo the editing and can't let my story sit for too long. Leaving a final editing round for 'the next day' is helpful though, because then you can more easily spot mistakes you overlooked earlier.
I, too, highlight or otherwise mark a word or phrase I want to use a better expression for, to get back to it later. That way I won't have to disturb the writing flow with editing or looking up words (sometimes I can't readily think of the right English word).
What I really like to use is the
Hemingway Editor. I tend to use too many adverbs and this is a great tool for me to pinpoint them and decide whether to remove them, tweak the sentence or decide it has its place. So I always run my finished stories through this editing tool first.
mianders:
How do you know when the time has come to leave it alone?
I don't. When I finish writing a story I format it in the way required for this site, do a last read to try to fix any remaining crazy typos, and then with trembling fingers I submit it. In between submitting and waiting for it to be loaded, I manage to successfully convince myself the story is terrible and everybody will hate it and there are probably embarrassing mistakes in there. And then once it's loaded, it only takes a single nice comment from a kind reader to make this whole sharing my writing thing worthwhile

mianders:
Do you worry about people who might not have English as a first language?
Absolutely not! Maybe because I am one myself. I trust other non-native speakers are just as good at finding Google translate or a dictionary as I am.
That said, the first story I shared here has French characters and a few French words thrown in. I did wonder if that was too much, because I don't translate them in the story, but I figured if it would be a problem, Flopsy would tell me to take them out. I haven't gotten any complaints about the French words, though it could be the readers who didn't understand them simply chose to abandon my story.
AlanBarr:
I don't see any need to make concessions for readers with English as a second language. They might quite enjoy being introduced to more obscure words or phrases, and it's easy enough to check meanings on the internet these days if it isn't obvious from the context.
This 100%