Where did the SHAKEs come from in SHA3?
Where did SHAKE128 and SHAKE256 originate from?


They follow from the general properties of the sponge construction. A sponge function can generate an arbitrary length of output. The submission of Keccak to the SHA-3 competition proposed a single "XOF" (extendable-output function) with a user defined length, which would have been essentially SHAKE-288. NIST seems to have decided on two instead, with more "normal" security levels.


  Any public cryptanalysis done on them?


Anything on the generic Keccak function may also apply to them. I don't know of any cryptanalysis specifically on the XOFs, beyond what was done by the authors themselves in the submissions and the site I linked above. However, a comment (pdf) to the draft standard complains that the usage of XOFs (i.e. SHAKEs) is not defined well enough and that their security claim is not very rigorously stated.