I will answer for the ages my DS1 & DD1 did these at.

Walk to school alone or with friend/s (one block or less) - We lived out of area for my kids school, so they walked to the shop which was a block away. Started to do this alone around age 9.
Walk to school alone or with friend/s (more than one block) - Walking to the shop further away - Only ever together and they were 9 & 12.
Catch public transport alone or with friend/s - 14
Stay home alone, during the day - 13, but when I was working and there was a gap of 1.5hrs between them arriving home from school & DH arriving home from work, they were 9 & 12 and our neighbour would check on them for us.
Stay home alone at night - 16.
Leave them to their own devices at home, while you sleep or whatever - DS2 kinda does this now and he is almost 5. I am able to trust him to not go out of the areas I allow him to be in when I am resting with the girls.