What they are going to do is find the necessary frequency to detect / view / hear Higg's invisible friend.
The question as to why Higgs can detect those frequencies may occupy a lower priority; and Higgs, being a skilled liar (it's part of his job), has probably already thought of 217 different explanations, and will choose one that seems likely to satisfy Rakethorne & Martellus.
EDIT:
Bang is going to try to kill Zeetha. It won't work. Possibly Zeetha will simply win; possibly someone will come by.
Possibly, she will deal "lethal" damage, and then we'll find out that the treatment Madame Zinka gave to Zeetha makes her as difficult to kill as a Jager - which is to say, she'll walk right up Bang's sword and beat her unconscious a la Madame von Pinn.
EDIT 2:
Or, she'll have her Spark breakthrough and use the materials at hand to defeat Bang.