Splitting a 220v line into a 110v line and a 220v line?
20A outlet on 30A circuit = no

The Code problem here has nothing to do with voltages and everything to do with currents. First off, 210.21(B)(3) and the associated table prohibit putting a 20A receptacle on a 30A branch circuit.  In addition to that, you can't run a receptacle off a tap conductor, as this is prohibited by 210.19(A)(2) (as well as being excluded by the list in 210.19(A)(4) exception 1):


  (2) Branch Circuits with More than One Receptacle. Conductors of branch circuits supplying more than one receptacle for cord-and-plug-connected portable loads shall have an
  ampacity of not less than the rating of the branch circuit.