So I had heard that Planescpe: Torment was a great game with a fantastic story etc. I picked it up in the D&D bundle and decided to play it first. So I had high expectations... and they have been met. This game is fantastic.
Only now ~15 hours into the game I keep running into weird problems with quests.
NOTE: There are probably some spoilers in here though I'm not too far yet.
So my quest bugs:

1: Tenement of Thieves: I talked to the girl who was trapped in there and I got the quest to go find the tenement key and leave. I did, the only problem being she didn't appear outside and the quest has not been completed in my log.

2: Clerk's Ward: I talked to the guy in the apothecary, I got him to make the vial of blood and skin for the dream maker, and it showed up in the dialogue "Gained Item" but I don't have it. I searched on the ground to see if it had been dropped because my inventory was full or something but no luck. I can't get him to make it again in the dialogue options either.

3: Clerk's Ward: I talked to Nemelle and then talked to Aelwyn and then to Nemelle again but the quest has not disappeared. I gained the XP and the HP bonus but the quest remains in the log.

4: Clerk's Ward: I've somehow ended up with a quest to help some guy with split personalities, only I haven't talked to anyone like that. It's just appeared in my quest log.

Any tips would be appreciated.
Now some questions:

1: Can someone point me in the direction of a valuable skull for Lothar? I've gone through all of the Weeping Stone Catacombs and I can't find anything. All I need is a little pointer, not a specific location.

2: How does the world map work? It pops up whenever I move between the lower and upper wards and there I can move to any location. I can also access it from the map screen, but it does nothing. It would be helpful if I could use it to quickly travel around.

3: Should I keep random stuff that people give me? I got a frost mug from the drunk wizard in the Clerk's Wards. It doesn't seem to be of much use. I'm not specifically asking about this piece but just in general, do random items from people help you out?

4: Are there any penalties to switching classes a lot? So far I've just switched from the starting fighter to a mage but now I've got Qui-Sai to teach me. I'm not a fighter right now though. As I understand it, I could switch to a fighter and get trained by him so I have those benefits and then switch back to a mage, correct?

5: About what % am I through the game if I am currently trying to find a valuable skull for Lothar? I know not very far but I'm curious.

Whew that was wall-of-text. If you can make it all the way through that and help me out, thanks!
Leonard03

Thanks for all your help. That clears up a lot! I have not installed any patches, it's just the straight version you get from GOG. Are there any you would recommend?

Bugs
2: You can use Infinity Engine Savegame Editor, and add the quest items to your inventory.

4: You have to buy a elixir to solve this quest. In this area, there's a store that sells exotic items, search there.

Questions
1:
Look in the Dead Nations for a human wearing a robe.

3: Keep it. Your followers can carry a lot of things, will take a while to have problems with space. If that happen, I think you can store items in the place you started the game, the one where you are teleported to, every time you dies.

The typical set is Quinn's Fixpack + Tweak Pack + Unfinished Business (and the widescreen mod + UI, if needed). You should NOT, under any circumstances, install anything midway through the game, however, so finish the vanilla playthrough first. PS:T is not that buggy, though the fixpack does repair a number of problematic quests and engine oddities (among other things), and has a bit of rule/balance tweaks (not that anyone plays this game for combat...).