From what I can gather, the new guy is someone she was seeing while attending "revenge" school. I guess he was seeking revenge on his sister's behalf but was too late to help her? At least I think that's what it was. Emily was going to go with him to help, but he left her behind.
As for it being Jack's baby, Emily just told Amanda that it wasn't his as a manipulation tactic. Emily wants to keep control of Amanda and what better way to do it than make her indebted to her by "fixing" her problem...even though Emily really didn't do anything.