Just started learning how to play this game and having a blast so far. I'm going to list a few questions I have, all help much appreciated and welcome.

1. How do I use my healer? How do I set up camp outside of town? All I know is that I can rest at inns until everyone is healed, or perhaps visit a healer or monk in town.

2. I just purchased fast horses for my entire group. How do I use them?

3. Is there a quest log? Or do I have to do this the old fashioned way, write everything down and take notes?

(I love this game! Everything about it, the setting, atmosphere, depth... definitely would like to see a remake. Just killed the raubritter Engelbert and retrieved Tarnhelm from a crypt for the pharmacist in Frankfurt)

"How do I use my healer?"
Healing skill automatically increases how much strength is restored per day when recovering at an inn/camp. It takes a lot of skill (30 iirc) to have any effect, but it's worth it.

"How do I set up camp outside of town?"
Press 'c'. I've heard F8 also works.

"I just purchased fast horses for my entire group. How do I use them?"
Make sure each person has one in their inventory and they should automatically be used, reducing travel time and such.

"Is there a quest log?"
Nope :(
Well there sort of is:
http://www.gog.com/en/forum/darklands/if_you_are_interested_inm_modding_darklands_this_is_what_it_needs_more_than_any/post4
But it might have problems:
http://www.gog.com/en/forum/darklands/if_you_are_interested_inm_modding_darklands_this_is_what_it_needs_more_than_any/post6

Thanks man. Doesn't seem to be any noticeable difference when using my horses.

Also, while regaining strength at an inn, I gain 2 str per day for each of my characters. My healer has a healing ability of 30. Without it being a 30, would my party receive only 1 str per day?

Yep, only one STR regained per day if you have a lower healing. I think the maximum is +6 per day.

As for no noticeable differences using horses- watch the day/night symbol, especially on roads. It doesn't make your sprite move any faster, but it can be handy if you need to get to a certain spot by a certain date.

I just snatched Tarnhelm from a crypt and have returned to the pharmacist in Frankfurt, but cannot reap my reward. It just goes to the shop menu. How do I turn in this quest?

Yeah, it's the right Frankfurt, only one I know of so far. Also, I left Frankfurt on this quest, stopped in at Speyer and picked it up there too for some reason, same one. I wonder if that newly acquired quest location canceled out the one I picked up at Frankfurt... hmm..

It happens at times that more clients require a certain item.
Stupid question (maybe), but... did you fulfill that second quest regarding the same crown, the one you got in Speyer (thus, did you get your reward there)? If so, you can't complete it in the first place you got it from, as you no longer have the crown.

Okay, figured out how to turn in the Tarnhelm quest... somehow... but now I'm stuck again. I met a dwarf in a mine that tells me below there are demons, and I have to kill the demons to free up the mine. Trouble is, I can't find a way to go down any further. What am I looking for?

edit: Nevermind, there was a hidden staircase that I could barely see.