with regards to applying early if you have all your materials ready to be sent i'd go ahead i'd ask members of your UG faculty their opinion as well though.
chem gre, if your a good test taker than seriously think about taking it if not and its optional then it might hurt more than help, honestly i sorta regrett taking it was not confortable with my result and think it might have hurt me with some of the schools i applied to , again ask your UG professors they know more about your abilities than any of us on a forum would