In my opinion it come with up because the upper eyelid is moving literally up when we open our eye !. so here there is a specific and only way that the open act is done within it, while when there is no specific and constant way to do that we just say open like open the bag....

No there's not much of a difference. Think of "open up your eyes" as "open your purse up" the opposite would be "Close your purse up" think of you purse as an eye. Hope this helps if you have any more questions feel free to ask. ☺

There is no difference.