As some pp have said, it would depend on a few things for me, maturity and personality of the individual child as well as where we live, the type of area we live.
I also can't really comment ofor my own kids yet, since they're only 4,3 and 1. But I will answer for myself when I was young.

Walk to school alone or with friend/s (one block or less) I think I was about 8 and it was with friends, if I had stayed with friends.

Walk to school alone or with friend/s (more than one block) 11, alone. I walked a 20min walk to and from school everyday.

Catch public transport alone or with friend/s. We moved when I was 13, so I started catching the bus alone to school then, but I assume mum would have let me do it younger than that had I needed to. About the same age, I was allowed to catch the train into the city with friends only, when I was about 15ish, I was allowed to do it alone.

Stay home alone, during the day About 10. I remember being sick (obviously not REALLY sick, I guess!!!) and mum let me stay home alone, but told both next door neighbours I was home, and they both came to look in on my.

Stay home alone at night I don't know if I was ever left home alone at night. I think there was always someone there! Though only by circumstance, I think mum would have left me alone at around 16 if she had to, but she never really went anywhere at night.

Leave them to their own devices at home, while you sleep or whatever I was probably about 7 or 8, and mum would leave me to do whatever when she got home from work, and go and have a shower and a sleep of an afternoon.

In saying all of that, I was pretty much a goody two shoes, lol. I never got into trouble and was (am!) very trustworthy and honest.