Can I use a copper ground with aluminum hot and neutral?
You can use the 10AWG copper for your EGC, provided the conductor is bare or insulated with a green or green + yellow stripes finish -- 250.118(A) doesn't say anything about not being able to use a grounding conductor made from a different metal than your circuit conductors:


  (1) A copper, aluminum, or copper-clad aluminum conductor. This conductor shall
  be solid or stranded; insulated, covered, or bare; and in the form of a wire or
  a busbar of any shape.


and Table 250.122 allows the use of 10AWG copper for the EGC of all circuits up to  60A in ampacity.  Since Table 310.15(B)(16) limits the ampacity of 6AWG aluminum THWN to 50A when in conduit, you'll be safe on that front.

HOWEVER, you must use receptacles of appropriate ampacity -- 15A receptacles are NOT allowed on 30 or 50A circuits!  This restriction comes from 210.21(B)(3) and the associated Table:


  Receptacle Ratings. Where connected to a branch circuit supplying two or more 
  receptacles or outlets, receptacle ratings shall conform to the values listed 
  in Table 210.21(B)(3), or, where rated higher than 50 amperes, the receptacle 
  rating shall not be less than the branch-circuit rating.


Furthermore, you cannot run lighting in a dwelling unit occupancy off a 30A circuit -- this is prohibited by 210.23(B):


  30-Ampere Branch Circuits. A 30-ampere branch circuit shall be permitted 
  to supply fixed lighting units with heavy-duty lampholders in other than a 
  dwelling unit(s) or utilization equipment in any occupancy. A rating of any
  one cord-and-plug-connected utilization equipment shall not exceed 80 percent 
  of the branch-circuit ampere rating.


You'd need to install a weatherproof subpanel by your driveway with the 6AWG Al as a feeder to do this, following 312.2 for the enclosure:


  Damp and Wet Locations. In damp or wet locations, surface-type enclosures 
  within the scope of this article shall be placed or equipped so as to prevent 
  moisture or water from entering and accumulating within the cabinet or cutout 
  box, and shall be mounted so there is at least 6-mm (1/4-in.) airspace between 
  the enclosure and the wall or other supporting surface. Enclosures installed 
  in wet locations shall be weatherproof. For enclosures in wet locations, 
  raceways or cables entering above the level of uninsulated live parts shall 
  use fittings listed for wet locations.


Once that subpanel is in place, you could then use 14/2 w/ ground UF or USE cable rated for direct burial to run standard 15A branch circuits to the outlet box and light fixtures.

Either that, or just pull a bunch of THWN copper through the conduit (ensuring it's appropriately sized, of course), and run multiple branch circuits.  You'll need at least 2 in this approach -- 1 15A for the lighting, and another branch circuit of the appropriate size to feed your outlets.