Wiring – What Happens When a Copper Wired Component is Introduced into an Antique Lamp with Aluminum Wiring

First off, the first electrician is wrong in saying that the use of a crimp-type terminal in house wiring is categorically unsafe. Crimp-type terminals listed under UL 486A for use on solid wire of the given gauge are considered acceptable for use in building wiring, as per UL 486A section 1.1:

These requirements cover pressure wire connectors and soldering lugs for use with copper conductors according to the National Electrical Code, NFPA 70.

and NEC 110.14(A):

Terminals. Connection of conductors to terminal parts shall ensure a thoroughly good connection without damaging the conductors and shall be made by means of pressure connectors (including set-screw type), solder lugs, or splices to flexible leads. Connection by means of wire-binding screws or studs and nuts that have upturned lugs or the equivalent shall be permitted for 10 AWG or smaller conductors.

Terminals for more than one conductor and terminals used to connect aluminum shall be so identified.

However, I would be quite hesitant to call this specific application fully Code-conformant -- garden-variety listed crimp terminals are listed for use with copper wire only, and it would be unlikely that the previous homeowner had access to terminals identified for use with aluminum wiring.

EDIT based on updated info about the devices:

Since the existing devices are copper only, your options go as follows (in order of preference):

1. Find an electrician in your area who is qualified on the Tyco/AMP COPALUM system for pigtailing copper to aluminum -- these have a long, successful field service history, but require a specially qualified electrician to install, and are rather expensive -- you might be able to get the seller to shell out for this, though...
2. Use the AlumiConn connectors with a torque screwdriver for pigtailing. This is something that most electricians can do, or you can DIY if you know your way around electricity and have a torque screwdriver -- the AlumiConn must be torqued to spec to meet its UL listing.
3. Replace all the devices with modern CO/ALR types. This is a last resort as CO/ALR device performance has been historically variable, unfortunately.

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.