Have a bath by themselves with door open / popping in.
4 with adult pottering close by on the same floor
Play at local park by themselves with adult crossing the road then going back to walk home.
If they’re not old enough to cross the road by themselves to get to the park then I don’t think I’d be happy to leave them there without an adult tbh. A local park right on the doorstep though, I’d say 6.
Go to local shop by themselves.
I’d say 8 generally though our “local” shop is @ a 12 minute walk each way with two busy roads to cross so in reality it’s something dd only started to do at 10.
Have a sleepover at a friends house.
The MN thing of sleepovers with various school friends isn’t something I’m familiar with, it doesn’t seem to be as much of a thing here. DCs had “sleepovers” with their cousins from age 3 though obviously that’s a family member so maybe doesn’t count. DD has sleepovers with her best friend and has done since @ 8/8.5 but we’d got to know her family well and have become friends. DS has only had sleepovers with cousins.
Have a play date at a friends house without a parent staying.
I’d say 4 but similar to the sleepover thing, formal, organised play dates aren’t so much of a thing and we tended to socialise mostly with family groups when ours were that age.
Play in back garden by themselves (large garden, can't see all of it from window)
From toddlerhood assuming enclosed, no obvious dangers like a pond, open garden shed or an escape route
. That said the back door would be open and parent in close proximity, checking regularly.
Play in whole garden including front by themselves.
Totally depends on how safe it is ie enclosed, is it a quiet street with neighbours you know or a busy one with lots of people walking past? Our front is mostly driveway so we stuck to the back garden.
Walk to school by themselves (5 minute walk, only road to cross is from our street onto the street the school is at, can be busy with parents but lots of people walking too).
8 though dc school a) isn’t walking distance and b) asks that an adult drop off and pick up until age 10.
Stay at home by themselves for 30 mins.
Either of mine would have been fine from 9 I think but in reality then 9 year old dd had a 7 year old brother so wouldn’t have been ok to leave both and now nearly 10 year old ds has an 11.5 year old sister so hasn’t been left alone. It just hasn’t come up that both dh and I and one dc all needed to be elsewhere at the same time.
Stay at home by themselves for 2 hours.10/11 depending on how sensible the child is*
Let themselves in after school for a couple of hours. 11
Stay at home by themselves all day. *My eldest or even both together (11.5 and nearly 10) would probably be ok now but I’d be more comfortable with 12 and even then preferably only the odd day and not every day for say, the school holidays.