Get a scalpel and remove 1/4" of insulation, look up the insulation. Wrap a turn of wire to tap into that bare section of copper. Put a piece of craft paper behind the tap so it doesn't short to the core (and possibly some black electrical tape. Not difficult.
Not that I could see. The OP only says he wants multiple taps at 10, 13, 16 and 19 turns. Without knowing the turns per volt, we really don't know what the voltages will be.
That said, the secondary voltage will be likely be low due to the relatively higher number of primary turns.