The girls are afraid of their punishment. You need to understand Puritan society to realize why their fear is so great. The Puritans were very strict, and children were expected to do as they were told and follow all rules. The Puritans literally expected children "to be seen and not heard". Most children will always try to figure the best way out of a situation with the least punishment when they've been caught doing something they shouldn't. Abigail and the other girls are no different, except their punishment could be as severe as being called witches. The Puritans lived in fear of the elements around them and saw the devil in anything they couldn't explain. The girls are right to be afraid of what they have been caught doing, and when they see a way out of it, they take it.
Ah, good question. The girls argue because they disagree about the best course of action, meaning specifically, which course of action would result in the least punishment for them. Mary wants to come clean, but Abigail wants to tell the adults a story.
Dramatically, this also sets up two sources of tension. First, there is a division between the generations (young vs. old), and second, Betty's claims that she can fly to her mother make viewers / readers wonder just how completely they believe in the witchcraft.