In fact, "zero LIBOR rates" can be obtain by interpolating from "Swap rates" for active maturities.
Following is an example:
Maturties(Years): 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 .....
Swap rates: a b (N/A) d (N/A) f (N/A) (N/A) (N/A) j
Zero LIBOR rates: a b c d e f g h i j
There are many type of interpolating algorithm, most usually used is standard cubic spline.
So could above serve as an answer to your first two questions?