I don’t have a ton of experience writing letters of recommendation but I have asked for many and seen how many are received. It is true that in the US, at least at the institutions I have attended or worked at, that an “okay” letter is often taken as a poor letter. Usually because the assumption is that the writer is being polite and is offering empty platitudes instead of outright saying the student is mediocre (or worse).
“Just” good letters (or letters that are overly conservative) usually get skimmed and the box ticked – that is they neither help nor hurt anyone.
It sounds like you want to write a great letter though. That is a bit of an art (I’ve worked with people who wrote great letters and others who didn’t despite their best efforts). The letters I have read that have stood out usually have a couple of key aspects 1) the letter writer clearly knows the student well 2) they have concrete examples of success and/or measurable comparisons to other students 3) they are written enthusiastically.
The first two should are relatively easy in the sense that when you have those things, the letter tends to write itself. Feel free to ask the student what they think their strengths are, what memorable moments in the lab/class they had, and anything they want you to highlight. These make good bullet points to weave together.
The third point is a bit of a style thing. Using stronger language is a start, but there is no need to write a cloying letter. Just be mindful that the way you normally write might need to be turned up a notch or two.
To answer your third point directly, this is what I meant by an “okay” letter. A writer may be obligated to provide something, or they may want the person gone (which requires them to be accepted elsewhere), or they may just not want to hurt any feelings by being upfront and saying they cannot write a strong letter. Letters like this are usually generic and dry. If it reads like the writer didn’t put effort into it or wasn’t enthusiastic, even if the letter says nothing explicitly bad, an admissions committee will read between the lines. As long as you make an effort to do the three things above, I doubt you’ll run into this issue.
As for your last question, when the letters are due is program dependant. I would just double check with the student what the program wants – it’s on them to know but you also shouldn’t assume. I don’t really know why you would intentionally send the letter late though. It would not weaken the letter necessarily, it just might not be accepted. In fact, there is a chance the application as a whole will be tossed.