1. Suck up = suck in - the action of a machine like a vacuum cleaner. In this case, it is her "campaign machine" which will quickly and efficiently raise funds for her..
"spit out soundbites" - "spit out" is what you do with chewing gum you have finished with or toothpaste water. This word suggests that the campaign machine will efficiently produce and publish soundbites (short messages with political meaning)
In this context, "fare" = perform, succeed. "against" is not part of a phrasal verb but is the correct preposition to indicate relation with an opponent.