Evolution happens through reproduction, which tends to happen earlier in life. So if some gene confers an advantage in early life but a disadvantage later on, it's likely the disadvantage won't stop it from spreading.
If it's not widespread, it's either not an advantage that "matters" or maybe it possibly has some negative interaction with other traits that matter for reproduction.
Humans have much longer lifespans than other animals, so it must be an advantage for our descendants to have us around. Presumably this is because of grandparents providing childcare.
That's not true - evolution is about the best genes for survivability and reproduction continuing to be passed along. The evolutionary perspective here wouldn't be that there are downsides to this, but rather that people with this mutation are better able to survive and reproduce, so we'd expect it to be passed onto more offspring over the generations.
Yes, this happens in the long run. In the short term, when a single gene has massive benefit, there must be some negative effect too, otherwise the entire population would quickly get that gene and that's not what we see here.
You are going to live long enough and be able to reproduce with about the same probability all other things equal whether you need 3 hours or 10 sleep nightly. There's very little evolutionary pressure even if you would massively and hugely prefer one of those over the other.
The kind of non-survival genetics that could be selected for in the modern world are those that make multiple women (nature can be pretty sexist) want to throw caution to the wind and have babies fathered by a man with some desirable attribute. I have no idea if this actually happens in reality with heritable genes. Eg do basketball players pass on a greater than average amount of their genetics (more children with more women) by virtue of being tall making them more sexually desirable to those who might become single mothers? Plausible, I guess, but could easily be utterly false. I don't know how you'd test it even in the absence of ethical concerns.
Maybe the downside is that someone who sleeps less will also tend to wander during the night, which increased the risk of dying before the modern world.
I think that's down to risk management skills of an individual. It could also be the case that sleeping less means you're more aware of external threats and ambushes and you can be more productive.