I don't read a lot of DC comics, only Marvel, but I can answer some of you're questions to the best of my abilities.
Spoilers if you care about this ****
Nightwing is Dick Grayson Aka the first Robin.
His parents(They were circus performers )got killed and Bruce Wayne (Batman) took him, trained him and turned him into his sidekick, Robin. Dick grew older, had a little fight with Batman and went solo for a while as Nightwing.
Jason Todd is the third Robin (I think) and yes, there are like 5 different Robins I think. Just like Dick, his parents die, Batman took him in, trained him and made him Robin. Jason is more of a " rougher" Robin(he breaks bad guys bones and put them into comas instead of just knocking them out like Batman or other Robins does.) Joker killed him, Ra's Al Gaul revived him and Jason turned into an Anti Hero known as Redhood. He found out that Batman didn't or couldn't killed Joker (Joker killed Him) and they fought and Jason/Redhood went solo.
Also, they both became Batman at some point, but went back to Nightwing and Redhood. And for some odd reason, everyone hates Redhood.
Earth 1 and 2 are just different universes, I believe.