Connecting together a rechargeable 1.2V battery to source current and a 9V battery only to boost voltage? Possible?

Output should be within acceptable voltages of a 5V/1A regulator. What would the schematic look like?

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I would recommend using a switching regulator on the 9V battery for increased efficiency (and longer battery life).  The linear variety burn off excess voltage as heat and effectively waste electricity.

As stated before, there really isn't a good way to use the 9V to boost the voltage of the rechargeable batteries.
better yet, a boost-buck regulator for the 1.2V
Possible, but given the current draw he would sap the batteries in no time.
 As steveastrouk says, "no."  Current flows from high voltage to low, so the battery would attempt to charge the 1.2V source.

If you have a 5V regulator, the 9V battery will work well with it, giving you an output of 5 v.  
No.