We never left our children alone at home at that age.
We did abandon them in the hotel bedroom for a couple of hours when they were 9 and 6. We were downstairs, actually in sight of the bedroom window because of the way the hotel was laid out. Left one of our phones with them.
We got them phones in year 6 ready for secondary, which seems to be most usual. Tablets whenever the Tesco Hudl came out - 2013 apparently, so 13 and 10. Before that they used the family desktop (we were mean parents who didn't think they needed a dedicated games console as well). Laptops couple of years later.
Playdate without me - reception?
Sleepover - I don't think they did them at primary school. Possibly once when S2 was in Y4. Apart from that the first would have been S1's in about Y10. It was a mixed one (never occurred to me till reading on MN that was an issue tbh).
Outside without supervision - back garden maybe 5ish? They never really Played Out, though S2 got called for by friends a couple of times in Year 6.
S2 was itching to walk to school by himself, but I refused until he managed to walk all the way there without walking along the kerb
. For most of Y5 I would walk as far as the main(ish) road with him. Round about Y6, so 10 and a half, I would let him walk to school entirely by himself. S1 didn't till secondary but he didn't seem to mind this. Oh, he did walk back from Friday youth club in Y6.
Go downstairs - 4 and 1 maybe? Though no, S1 was going down by himself before that. He would put on the tv or a DVD and watch Thomas, Thunderbirds or Milkshake.
He once climbed onto the worktop to get a mug out of the cupboard to get himself some milk. Aged about 3 (oops). We said he probably shouldn't do that again. Apart from that, they tended to wait till I came down and got breakfast (they're both perfectly capable of feeding themselves now).
Bath/shower - not sure. We used to shower after swimming at the health club. Really can't remember when I was able to leave them to it.