#1
Is the purpose of the crybaby just to be a whammy bar using your feet and not your hands? or is there something im missing?
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#3
whammy bar and a wah-wah pedal are entirely different. Your whammy raises and lowers the pitch of the note where a wah is changing the signal and produces the wah effect on the notes you play
#4
yes, there's something you're missing. a crybaby is a wah pedal, its basically a filter effect, it does not do anything to the pitch.
Rig Winter 2017:

Fender Jazzmaster/Yamaha SG1000
Boss TU-3, DS-2, CS-3, EHX small stone, Danelectro delay
Laney VC30-112 with G12H30 speaker, or Session Rockette 30 for smaller gigs
Elixir Nanoweb 11-49 strings, Dunlop Jazz III XL picks
Shure SM57 mic in front of the amp