I'm going to answer the first part. It's the hardest, but also the thing people are most confused about. So here goes.
Elvenar is a city building and management game. You have all kinds of things to manage and just about everything takes some resources. So creating those resources at the highest levels is what you focus on. In general most players end up managing "catering" cities (cities that do what they do through the use of goods and other resources over using troops) or military cities. All cities are, by necessity, both, but you can emphasize one or the other. Remember, since it's production that determine the speed and strength of your city, you want to maximze production. There are two ways: Produce more and use less. The Cauldron is a way to produce more.
So, first you have to look at the effects (temporary improvements) you have available for you in the cauldron. These are potential effects that can be triggered by brewing a potion for them. If you are military minded player you will probably focus on the effects that impact the military. If you are a "catering" player you will look at the catering effects. The list of effects only grows, it does not shrink. It is based upon what chapters you've completed. One per chapter. The farther you go in the game the longer the list gets.
Once you have determined what effect you wish to trigger, you have to create a potion for it. You have Witch Points to use and can spend them on the various ingredients needed to brew your potion. The amount of witch points depends on how much research you have done, including researches past the end of the last chapter.
The whole, "which ingredients do I use?," question is still being hashed out, but, so far it seems the best way is to focus on one effect, find the ingredient which has the greatest impact on it per witch point spent (you can tell by looking at the list of effects on the right as you choose ingredients) and then going on and trying each ingredient until you find the one that increases the effect the most. Keep going until you run out of witch points. Now, oddly enough, you will then have to write down which ingredients you used and how many of each. Usually you will use 4 to 6 ingredients and up to seven times for each. In any case, at this point you empty the Cauldron and re-enter the ingredients beginning with the one you use the most. So if you use 6 bitterleaf, 4 Nightshade Blossom, and 3 Mana Shells, you would enter them in that order. The difference is, when you created the recipe you may have entered a bitterleaf, then a mana shell, then a Nightshade Blossom, then two bitterleaf, and so on. But it's cheaper to reenter them after finding out which give you the best "bang for the buck".
When you brew your potions you will have one to five chances of it working. The one to five depends on how you did in the tournament . As you do the tournament you can see how many Cauldron chances you will have by watching your Trophy Goblet progress in the tournament report screen. So, in essence, if you have brewed a potion you like you will have up to five chances for it to take effect. Notice, as well, that while you may have focused your attention on one particular effect, other effects are possible. The list on the right lists all the possible ones and their chances for the week.
That's the basics. But there are three other things to consider. First, you can add Spell fragments to your recipe before brewing to increase it's "critical effect chance". This is the chance that if one of your brewing chances (the number of goblets -- the "roles of the dice" you use) triggers an effect and that the level of the effect will be at the maximum. Since each potion that does get triggered is somewhat random as to it's strength, the "critical effect chance" increases the chance it will get triggered at it's highest possible strength and duration. Second, with each ingredient you increase the chance of your effect being triggered by 5%. So the more ingredients the better. And third, you can permanently improve (i.e. raise) the highest strength and duration of each effect after you brew them each week. Returning to the Cauldron screen allows you to use all kinds of ingredients to improve maximum of the selected effect. Warning: every time you use a resource to raise the maximum effect the next time you use that ingredient it costs more. AND, the improvement won't show up until the next week.
Finally, some caveats. First, you can skip the diamonds if you wish. However, if you do, the chance of triggering the effect you want may not be nearly as strong since each effect has a favored bunch of ingredients and some of those ingredients may need diamonds this week. So don't be afraid to switch which effects you want to trigger.
Second, since the potions take effect the moment you drink them, be sure to drink them at the right time. Unfortunately, that means you will need to write down the recipe you find and remember to use it at the right time. Often the duration of the effect is so small that it's pretty easy to trigger it at a time you can't use it only to have it expire before you can! Argggg....
Hope this helps.
AJ