Both a:s in långsammare should be short: http://sv.forvo.com/search-sv/l%C3%A5ngsammare/
Is this technically an adverb? (Just wondering because it affects how I order my note taking)
Yes. Adverbs compare the same way as adjectives.
why cant say "she speaks slower now"?
Why not "she speaks slowly now"? Where does "more" come from?
Slowly = Långsamt
Slower = Långsammare
The suffix '-are' is similar to the suffix '-er' in english.
So it could also be translated 'she speaks slower now'