Assuming you ignore or amortize the time necessary to create the table in the first place, of course.
This is the basis for rainbow tables: precomputed tables for mapping hashes to passwords, with a space-saving “hash chaining” trick to effect a constant factor reduction in table size. Such tables are the reason why passwords must be hashed with a unique salt when stored in a database.
I’m not sure this definition of Big-O for space complexity is universal. When I’ve seen/used it, the size of the initial data wasn’t relevant, it was more about the additional memory required for the algorithm.
For example, an in-place algorithm like Bubble Sort would have a O(1) space complexity, because it requires no extra memory (and 0 memory is a constant). Merge sort on the other hand is O(n) because it always uses additional memory for its intermediate stages, and that additional memory scales with n.
Very. For instance if you look at sorting algorithms on wikipedia they pretty much all list performance (best, worst, average) but also worst-case space complexity, in O notation.
...oops