How to compare one time pad security and efficiency with AES?
Answer 1:  If you are going to use a "one time pad", then $c1$ must be exactly the same size as $m$, so $c1$ must be 32 bits.  (Note:  Using a PRF and evaluating with the input of 0 is not a one-time pad.  It might be equivalent if you change $k_i$ every time, but then why bother with the PRF when you could use $k_i$ directly?)

Answer 2:  Since you specific it as a PRP (pseudorandom permutation), $c2$ must be 32-bits.  With a permutation, the size of the input matches the size of the output.  A PRP pseudorandomly maps each element of the possible input set to a single item in the output set.  So as with the first, $m$ and $c$ must be exactly the same size.  

Answer 3: There isn't sufficient information about the rest of the system or usage to really comment on their security with the exception to say:  trying to make a "one-time pad" from other function almost always fails and anything that has only a 32-bit input can probably be trivially brute forced.