1. It's a problem and a matter of knowledge. As you know, every of your guys is playing his own game. For example, if you want three of your guys to do a certain quest then each of these guys must get the quest and complete it somehow.
Some quests can be "serialized", that means, that you can use the method "get the quest - finish the quest" repeatedly and let any number of your guys to finish the quest this way. Some quests - most often those quests that involve killing a "criminal" somewhere - cannot be serialized. Once the "criminal" is dead, you cannot get the quest again. These quests must be done "at once", that means, all adepts of the quest must take the quest at once, then the "criminal" needs to be killed, and then all the quest owners will be rewarded (again at once). There are also a few quests in the game that can be done only once and by only one character - providing you are not about to play tricks on the game

- the assassin quest is an example of these quests.
The only thing that matters for the quests of the type "bring something from somewhere" is the quest item in the right inventory. It does not matter how and when you have got the quest item. But the quest item usually appears only if the quest owner is present in the adventuring party.
Here are the quest conditions for the Valeia and Ishad N'ha quests.
Valeia:
Temple:
- Medakwa: The quest owner must give the potion to Medakwa.
- Donation: Can be serialized.
- Ring of Saints: IIRC, it can be serialized. The ring reappears whenewer you get the quest. At any rate, the quest owner must be present in the Crypt when you go for the ring.
- Paladin promotion: The quest owner must pray at the statue.
- Warlock promotion: The ownership of the egg and the skull is the only thing that matters. Where the quest owner has got them isn't essential. Can be serialized. Every egg and skull will do, the quest owner can even sit in the inn and send others to kill some spiders and skeletons.
Mages Guild:
- Scabban: Should be done "at once" because it often involves killing Scabban. Even if you let him live, the bugs in the game can cause that you'll be unable to get your reward.
- Talrik Teporn: Must be done "at once".
- Orb of Clarity: Must be done "at once" - even if the only thing that matters is the Orb in your inventory. The problem consists in the fact that there is only one Orb of Clarity in the game during each game run. On the other hand, it does not matter how and when you have got the orb.
- Warlock promotion: see the Temple.
Warrior Guild:
- Mon the Sculz: Must be done "at once".
- Toad willage: Can be serialized.
- Sword of Mastus: Can be serialized but the owner of the quest must be present in the Crypt when you go for the sword.
- Barbarian promotion: Can be serialized.
- Ranger promotion: Can be serialized. Every time you get the quest, a new raptor is spawned and new two eggs appear in the game. You will find the raptor only if the quest owner is present. On the other hand, the egg in your inventory is the only thing that matters. It isn't essential how you have got the egg.
Ishad N'Ha
Temple:
- Xydusa: Must be done "at once".
- Scroll of Galian: I am not sure whether this quest can be serialized. The scoll is in a chest and I am not sure whether it will reappear in an open chest. You'd better do it "at once".
- Jathil: Can be serialized.
- Monk Promotion: Can be serialized.
Mages Guild:
- Ardibren's Keepsake: The same problem as with the Scroll of Galian. You'd better do it "at once".
- Idol of Aku: Can be serialized.
- Collanth: Must be done "at once".
The Pawnshop:
- 10 serpins: Can be serialized.
- Ardibren's Journal and the Band of Boars: The same problem as with the scroll of Galian. You'd better do it "at once".
- Bard promotion: Can be serialized. The scroll reappears every time you get the quest but the quest owner must be present when you go for the scroll.
Bushi Dojo:
- Dragon Arrow: Can be serialized.
- Thorin: Can be serialized.
- Shrew Chishi: Must be done "at once".
- Ninja promotion: Can be serialized.
- Samurai promotion: Can be serialized. Every time you get the quest, a new samurai ghost is spawned and a new batton appears in the game.
2. Yes, the quest items will be often taken by the questgiver. In most cases, it's no loss. Most quest items in W&W are plain quest items - useless or low value items, only intended to be given to the questgiver. But there are exceptions

Also, losing the quest item can prevent other characters from completing the quest because the quest item was unique. The tricks with quest items you have read about in other threads are attempts to "fix" it
3. The main reward for qests is the advancement in the corresponding guild. The higher is you guild level, the more skills you can learn and train in the guild and the more traits you can get there. The few XP (and, sometimes, money), which you get for the quest are rather unessential.