I take it you're hoping to poke sticks of conduit up from the basement and hope to come out in the attic without hitting anything? It could happen, but I'd be rather surprised. 1.5" conduit is fairly chunky, I think you're likely to hit something. If you wanted to fish a few runs of Cat 6 I'd say your chances were good. But conduit? (BTW, bonus points for knowing better than trying to run inside the duct.)
Even if there's obstructions, it may be possible to make the run by cutting discrete access holes to cut out the obstructions, assuming they are non-structural. If you haven't yet done so, examine each floor carefully to determine if there's enough space to even make the run. Measure carefully to arrive at accurate void dimensions, and ensure the proposed run aligns on each floor, which may not be that simple. Once you've determined it's feasible, start pushing pipe, keeping track how much length is pushed up. You'll likely hit something. Figure out where it is vertically. Gain access and clear the obstruction. Repeat as necessary until the attic is reached. Good Luck!
First off, you likely want type UF cable for this application -- URD isn't even a recognized NEC type to begin with, and even URD/USE cable can't be run indoors as per 338.12(B)(1) as it lacks the fire-resistive insulation of NM, UF, and SE cables.
Second -- while 2AWG copper USE has an ampacity of 115A as per the NEC, since you cannot use USE in this application, you must use 1AWG wire here, as UF has a lower temperature rating than USE (60deg vs USE's 75deg) and thus a lower ampacity (2AWG copper UF can only carry 95A, while 1AWG copper UF is limited to 110A). This may also require you to upsize to 2" conduit in order to keep the conduit fill acceptable. Of course, since you are doing the run in conduit, 2AWG copper THWN is also an acceptable choice of wire for this task, provided the indoor run is done in conduit as well, and would allow you to keep the existing 1.5" conduit.
As to the neutral and ground wires, a 2-2-2-4 configuration would be used -- this is as per 215.2(A)(1) Exception 2, which would prevent an undersized neutral in your situation when the feeder is fully loaded. Of course, 2-2-2-2 is also acceptable, and may be easier to manage when working with individual THWN wires in conduit.
If you do decide to use URD/USE for the outdoor run -- you will need to use a different wire type for the run indoors. You'll either want copper THHN/THWN in conduit (2AWG works), or a 2-2-2-4 copper SE (note, NOT USE) cable, either in conduit or run as if it were NM.
Best Answer
Screw to the studs, behind the siding - you can screw through the siding, but expecting screws to hold in (just) siding is foolishness.
Look for the fasteners that are holding the siding in place to indicate where the studs are. Use screws (or short lag bolts) about an inch longer than the siding is thick.