I think "hurry up" is more rush and more clueless than "speed up" , for example , someone should hurry up to catch up with his class or bus because there is little time left and the point of time is specific(can not be changed) , while "speed up " can help to save time .

"speed it up" might be okay if you are referring to a machine, meaning to make it run faster.

Yes but "hurry it up" is more common.