we are still in the 3s. DS was 3 in August and even before that he would cry about not being able to watch tv, or having to pack up toys, eat tea you name it we get it.
While it might be frowned apon if he is crying for no reason we either make him go to his room or we leave the room and say we will see you again when your finished crying and that you only cry when something really sad happens or you are hurt.
he calms down quicker when he has no audience.
he is more likley to bung it on when he is tired and or hungry.

re the possessive behaviour ds isn't too bad, he has been proclaiming a few things t be his, but as he was not the very first child born for either side of our family he has always been forced to share toys and people.
My niece throws herself to the floor and does the full on leg kicking etc, so i'm glad we don't have that.

My sil had had enough with her 3 yo (different niece) about 6 months ago now that she took every single possession away for 24hrs. Her bedroom was stark white, even the doona cover was taken away, but she did learn.

I think the trouble with 3 is that they have started to learn and push boundaries.

I feel for you and know just how frustrated you must be right now, I struggle most days to remember to reward good behaviour and ignore bad behaviour, and I have the niggling little thought that whoever wins the battle this year will impact on how he behaves as he grows up. 'cause he will know which buttons to push iykwim

Good luck