All cuts should be vertical and in any direction ... I only emphasized that no horizontal cut is allowed, e.g. one could possibly divide a cake with three cuts to yield 8 pieces ... 2 vertical cuts and 1 horizontal cut!
(1) 125251 pieces after 500 cuts (correct)
(2) 3162 cuts gives 500704 pieces (also correct)
(3) Never mind the 3rd answer since I reckon that it must be infinity, although 199999 cuts as a first approximation comes very, very close! However, there will always be a remainder of either 1 or a pretty large number.
Therefore, 2 remains the minimum and maximum pieces-to-cuts ratio. I cannot, though, prove this mathematically (yet)!
I wasn't aware of an entry at "Mathworld"! So, my question should actually have been a straight-forward quickie!