"The Solitaire cryptographic algorithm was designed by Bruce
Schneier at the request of Neal Stephenson for use by field
agents in his novel Cryptonomicon, enabling them to
communicate securely without having to rely on electronics or
having to carry incriminating tools, It was designed to be a
manual cryptosystem calculated with an ordinary deck of
playing cards. In Cryptonomicon, this algorithm was
originally called Pontifex to hide the fact that it involved
playing cards."Which shows that these numbers don't at all measure puzzle difficulty.
It depends on your definition of sorting. Since we have a known, finite, compact set of incoming inputs, essentially the numbers 1-52, as rocqua says we can use a bin sort with 52 bins and sort the cards in essentially 52 operations. This is physically practical as well. Generally the "constant overhead" on it is such that people will sort with something more like a merge sort, but it's certainly completely practical to find a space large enough to hold the entire deck laid out physically.
If you limit sorting to the computer science sense of the term, in which the sort must be accomplished by swaps, I expect it could be worked out pretty easily by people skilled in the art of sorting, again because the small constant size and input makes it relatively easy. I know it can be proved that this style of sort can't take less than O(n log n) comparisons, but I'm not 100% sure I can guarantee it's literally ciel(52 * log2 52). Somebody else may be able to.
I think the simplest answer is 52. You need to place each card correctly once. Things get complicated if you account for searching in the deck, but we don't account for looking at the rubiks cube either.
A more interesting question is 'what if we count how far we need to move the card' (i.e. moving it from position 1 to 52 is 52 steps, and from 1 to 3 is only 2 steps).
This is a question of simple group theory though. Shuffling cards is the group S_52. The 'moving a card one position' is working with 51 simple operations of swap (idx, idx + 1). This is essentially bubble sort.
Yes, obviously the solver has to understand what the desired solved state is in each case.
If you can't see that sorting a deck of cards is easier, I doubt I can explain it to you, but the metric I'd use is give each problem to 100 people, and see how well each group does.