My first language is Korean, and one rule no one gets right is the spacing. It seems pretty obvious in English and many other languages, but in Korean, there are things that look like a single word but is actually two separate words (and vice versa), particles which needs to be written without spacing, and some other rules that makes it confusing. It’s bad enough that one of the former director of the National Institute of Korean Language confessed he’s not confident about it either.

I was going to say, “Don’t end a sentence with a preposition.”
However, this rule is heavily debated and mostly defunct now, it seems. It does make a sentence sound more formal, though, so sometimes I use it that way.
The one I’ll mention instead is “I could care less” as opposed to “I couldn’t care less”, but only as a preamble to the one I really want to say (ahem). I think most people now agree that “I could care less” does not usually convey what the speaker means to say, and that “I couldn’t care less” is usually correct.
In the same vein, “I’m going to try and do something” should almost always be “I’m going to try to do something”. Because, if you try and do something, then you don’t need the “try”, you’re just going to do it. By saying “and” you’ve presupposed you’re going to succeed, making the “try” redundant. But, if you try to do something (as in moving toward a goal), that means you don’t know whether you’ll succeed. I know I’ve lost this one, because “try and do” is so ubiquitous now. Just like we’re losing the word “envy” in favor of “jealousy” used incorrectly, and the distinction between less and fewer is all but forgotten.
Don’t get me started on “affect” and “effect”.
If someone says “I could care less” I finish it in my head with “but it would be really difficult” and all thing are right in the world.
Tongue in cheek, try and do something could still be correct. I’m going to try, if I fail, I’m going to have a beer.
I think the preposition thing comes from people who learned Latin (and a long time ago, 1700’s) - I think you simply can’t end a Latin phrase with a preposition because of how sentences are constructed.
Your other examples grind my gears too.
Less and fewer are like fingernails on a chalkboard for me.
Same! Then and than, too…shiver.