With Alchemist, you are limited to having a single Attack spell from Alchemist, That one arent really good since you have to use one dropped item (loot) for it to work, or if there is no loot you can upgrade a passive which makes it cast but you lose 200 silver.
Dig, its plain and simple. You dig for items, not always anything valuable. Usually rock, or ingredients used for flask crafting. So no, Its not important at all really, unless you want to dig?
Tincturing is the Flask crafting, as the other lad mentioned level 1 tincturing is 10% better than what you can purchase. Now I can’t really remember the cost of ingredients if you were to purchase the ingredients from the alchemist trainer or not, but from what i remember it took 20 seconds to craft 1 recipe of life/SP flask (5 flasks per recipe).
Then to craft a large amount of flasks required you to waste quite some time, but of course you could sell it afterwards or use it as you go.
Higher the level of tincturing the bigger the variety of flasks you could craft. It could all be from Stamina Pill, Increase Crit Chance, Increase Magic Penetration and such, So every level of Tincturing would give you a new recipe.
Item Awakening, to enhance an item by creating a dungeon for that item you want to awaken. Clear x-amount of waves of monsters + a boss in the end. The stats can vary when the item has been successfully awoken. Usually requires a party of sorts if you dont have a solo build of sorts (pyro2 - linker2 for instance)
Briquetting is a neat option for us alchemists, we can enhace a weapon by reducing or increasing the damage by -% to a positive % (from -5% to 5% or -9.5% to 9.5%), so its a gamble to boost your item. Proceed with cautious
Gem Roasting is then the reducing the penalty on gems you put on gear/weapon, (the penalty would then be all the negative values will be reduced on the gem).
Magnum Opus is quite an unknown skill still, As far as I know, there are no recipe site which states what item one can craft with the skill, since its just a grid and you are free to place item in what order you want or figurine*.
Thats as far as all the alchemist skills work in theory. Now the hard part is really to figure out how to get yourself down the road to become an alchemist. Alot of people feel very limited to what to build in terms of damage, support or just a jack of all trade to get down to alchemist. Find a “dps/support” class that fits you (if you are a solo player or group player), and then walk down that road.
I hope I could aid you a bit with a simple understanding towards the brewmaker.