access the auto filter list

with the auto filter on
simply highlight those cells(rows) set print area and print
it will then print only those visible from the filter result
as for drop down
i take it your using a validation list.
you can always just extend the range of tha validation. or build the list
with some capacity for new wntries.
say you have 5 things and your list is
=$C$1:$C$5
you could simply first build it as

=$C$1:$C$30
this gives 25 blanks at the bottom
which you could just add to eg put something in c6 then c7 etc as required