That conductive ink stuff tends to go everywhere. Mask off anything you don't want it contacting with tape before you start.
As to removing the LPC header:
1) grasp pin on top side of board with neelde nose pliars.
2) gently pull
3) while pulling GENTLY, re-flow the solder with the iron. The pin should heat and pull through the plastic as soon as the solder melts.
4) repeat.
5) once all pins are out (the plastic having come up with the last one), apply a thin layer of flux to the LPC header through holes, lay the tip of the clean solder braid over one through hole, apply heat from the soldering iron to the braid. Once the solder wicks into the braid cut off the saturated part. repeat for all solder you want removed.
Honestly though, send the board and your chip to me and it will come back in stellar condition, chip ready to go.
-nB