Lockpick can be learned up to level 11 in the main game, and to level 20 in the after game battlefields. Doors usually have a key or lever to open. IIRC, there were only a handful of chests and one small room (with a chest to loot) unavailable when Lockpick was not working, so I think not using the skill would just cut down on the random loot. I have not played that much since the latest patch was released, though, so don't have much experience with Lockpick.
In DD Lockpick was useful on more doors, and was required for a couple quests. Had you opened the locked chests as you went, some of that loot might have been more helpful. At least at the start of the game I upgraded my equipment a couple times from locked chests. Towards the end of the game you already have pretty much the best equipment you will get, and have no need of more loot to trade with.
As long as your mage is not taking too much damage you can stick to melee, though having a secondary character set to aggressive with a bow can be handy. They can start shooting at opponents that are still a little off screen, giving you a bit of advanced warning that an enemy is close by, and in what direction. A distance attack (magic or archery) is also good to have fighting enemy archers or mages. Mages especially can use hit and run tactics, so warriors can take a lot of damage running after a mage trying to get a hit in. The tibars in act 2 jump around a lot, so if you attack one (turning them all hostile) a bow really helps in dealing with them.
The skeletons in the first part of act 1 take more damage from blunt weapons. I started off with two melee warriors, with one using a bow for some of the tougher fights. Towards the end of act 1, I switched one character to a full time archer.
Summoning dolls are at least great mules, and they can safely trigger area effect traps (or at least safely for you). The weight penalty was changed in the latest patch, so you can carry as much as you want, but can not move when over encumbered. Since the summoning dolls can be summoned and unsummoned wherever you wish, there is not much need for them to move (they have a limited range anyway, without being upgraded).
The act 1 skeleton doll can equip a crossbow, which can be helpful for tough fights, though it is not very strong even after being upgraded, so will not last long if your opponents start targeting it (though it that case it is at least a temporary distraction).
There is one summoning doll in each of the 4 acts of the main game. The act 1 doll is a quest reward on the second level of the game (with the 2 imps in the kitchen, after you jump down the pit).
When you check the summoning doll's inventory, there will be 2 levels you can upgrade it. This is a communal pool, so you can either boost the first doll's level, or leave those levels until you get stronger dolls, and upgrade them.
Since the point of the game is to separate yourself from the DK, it would probably be better to have the DK learn any summoning doll upgrade skills (they can not be unlearned). Near the end of the game I had my DK unlearn all his skills and put everything into the summoning doll upgrades, so I could play around in the after game BF with the hero and skeleton doll. Before then I had only used summoning dolls to fight a couple times, and had not upgraded any of them.
I pretty much only used alchemy in BD near the end of the game, when I finally found holy water for sale by the BF merchants, and could use those (and the one received earlier from a quest) to make some permanent potions (for my hero, since the DK was soon to be separated). Before that I was stashing alchemy plants on a summoning doll, so had lots.
Mushrooms are just for looks / atmosphere in BD.