It's both, but primarily it's geography. It's also both about administration and representation, but mostly the former. If the population of Alaska were placed in a 10 square mile area completely engulfed in another state, then statehood would be questionable. You're introducing a lot of overhead versus keeping that area as a single state. On the other hand, you could reduce the population of Alaska to a quarter of its present level and statehood would still be easily justified based on geography and sheer size.
Arguably, certain states like Rode Island and Delaware don't need to be states based mostly on geography, and others like California could be two or more states based on population and the fact that there's plenty of land mass to go around.
It might. You're not breaking the literal written letter of the law, but you're still violating the spirit. It's not difficult to make an argument that, stripping D.C. down to the core buildings of government while granting the surrounding area statehood would still leave the federal government largely beholden to this new entity, which is exactly what the constitution is trying to avoid.
I would not be at all surprised if that, combined with the sheer naked opportunism of the move, given that for the purpose of granting better representation to D.C residents giving land back to Virginia makes more sense administratively and yields less risk to the autonomy of the federal government, might be enough to sway the conservative justices.
It could even be enough to sway some of the liberal justices. After all, taken to it's logical extreme, any party that controls the house, senate, and presidency in the future can, at a whim, create a multitude of new states out of thin air such that the party will never lose control of the senate. And if you don't think that, should Republicans gain such control of the levers of power after Democrats grant themselves two permanent senators that they aren't liable to do exactly that, then you're naive.
It's the same reason why expanding the size of the supreme court to pack it with your cronies is such a bad idea. These kinds of moves only serve to destabilise a nation where people are already at one another's throats.