Hello and welcome!
1) The only way to defeat the ghost is to place to sword back into the stone. If you take the sword, the ghost will roam free and kill all NPC's in the Dark Forest except for main-quest essential characters. It's a choice you have to make.
2) There are levers on the walls for these doors. Look at
this map. (#'s 6a and 7a)
3) If you overheard the woman gossiping in the streets, then you know to ask for Magadalena or Yaniz. Talk to Afrasam at the Ducal Inn and reveal the passphrase. He'll direct you Leptine's store, and you should be able to manage the rest and report back to the brothers at the inn.
