Exactly, only the one with FAX can do that.

No, the HP 4302dw is NOT capable of two-sided scanning via the document feeder, the HP 4302fdn or HP 4302fdw must be used for this.

According to the data sheet, not "Double-sided scanning with automatic document feeder (ADF): No" the answer from sugus3434 seems to be correct.

Theoretically yes - but it has trouble pushing the paper properly - in my case it always led to paper jams in the document feeder

Yes