It's going to vary between households, but this is what happened in my house as a child.
Stocking is instead of the sack, but are individual, each family member or each child has one (Just kids in our family)
They get placed on the end of the bed on Christmas Eve, and a plate with mince pie/milk/carrot left out for Santa somewhere in the bedroom (my sister and I shared a room - some people leave stockings by fireplace, or on door handles, etc and leave mince pie/carrot in living room)
In stockings are small presents, nothing from the list, just silly things, usually some sweets and always some chocolate coins, and then things like hair bobbles, crayons, stick on tattoos, handbag mirror, little pack of cards or mini game, mini activity book etc etc. It's bigger than a sock so you can fit small wrapped presents in, but not as big as a sack, so nothing larger than a large orange would fit in. No CDs or DVDs or books or anything (those were usually main presents though as used to be more expensive) - Some people don't wrap the stocking gifts and some people stick to a theme of everything having to appear hand made by elves 
Under the tree are presents from family (including parents) and some from Father Christmas. My mum would split about half and half what was from her and what was from FC, it didn't seem to follow a pattern about what FC brought and what parents brought.
Oh, and she would also hide most of the presents, so that on Christmas morning it was a big exciting thing to go down and see the pile had increased significantly!
Stockings would usually be opened in our bedroom alone, there's something about wriggling your feet down in bed to feel the weight of it there and hear the crunch of the paper, knowing that it had been filled! DSis and I used to have an agreement about when was too early to wake the other up, and if you woke up early it was agony! We usually had the same things in different colours in our stockings so we'd open them at the same time to avoid spoiling the surprise. Then we'd go and wake up our mum and show her what we'd got
Tree presents would be opened at some point during the day itself, the time varied.