I had never heard the expression "reply back," but I just came across it on this site: English Editing Experts - Proofreading and Translations.
"Reply back" sounds redundant to me. Isn't "back" implicit in "reply"?
I agree. That it's on a site offering to proofread your material for a fee is, to say the least, ironic.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.