The moisture level of the cheese is mostly determined by what you do when you make it. "Flocculation Time" is the amount of time between when you add the rennet and the curd first forms. You will *never* cut it at the flocculation time. Flocculation time is a bit of an imprecise measure and it varies from cheese make to cheese maker. I *believe* this technique originate with Peter Dixon, but I could be wrong.
Basically what you do is that you add your rennet, stir and then float something on top of it (I use a cap from a soda bottle or a wine bottle, but you could use a milk cap if your milk comes in those kinds of containers). Every minute or so you spin the cap. When it stops spinning, then the milk has "flocculated". I actually wait until there is a mark left in the milk when I remove the cap. That's a bit longer than most people, but I find the measurement is more consistent because there is a concrete thing to look for.
Anyway, that's the "flocculation time". Depending on the amount of rennet, the acidity of the milk and the temperature your flocculation time will be anywhere from about 7 minutes to 20 minutes. It's kind of an advanced topic for why you might want to shoot for different flocculation targets, however, 12-15 minutes is pretty typically what you want to aim for.
After that you have a "flocculation multiplier". That's how many "flocculation times" your total from adding rennet to cutting will be. A flocculation multiplier of 1.0 is just the flocculation time. 2.0 is twice the flocculation time. 3.0 is three times, etc. Most cheeses are in the 2.5 - 3.0 range. The time you cut the curds gives you the biggest impact on the moisture level of the final cheese.
I think the easiest way to think about this is imagine cutting milk with a knife. Your knife cuts right through it :-) If your drain that and collect the curds you get *nothing*. It just drains away. That's the driest cheese you can get :-) Now imagine a gel that is like rubber. You cut the cheese and it cuts just like rubber. Nothing leaks out. That's the most moist cheese you can get (it retains 100%) of the water. It's a bit weird, but you can see that soft curd will give you a dry cheese (because the water will leak out) and a hard curd will give you a moist cheese (because the curds will hold the water).
That means that the larger the multiplier, the more moist your cheese will be. The smallest useful multiplier is 2.0. That's used for cheeses like Parmesan. Once you get to a multiplier of 5.0 then it's pretty much as moist as you can get. There is one small caveat. Once you get to a multiplier above 4.0, when you cut the curds, they are hard enough that they will tear. Because the tear is jagged, whey will actually leak out *faster* than a cheese with a smaller multiplier. It just means that if you are doing a very high moisture cheese, there is a practical limit on how long you should wait (there are other factors as well).
The next biggest place you can control moisture is with the size of your curds. The bigger pieces you cut your curds, the more moisture they will hold. If you are cutting them in 2 inch (5 cm) cubes, they will leak whey *much* slower than if you do 1/4 inch (1.25 cm). That's because smaller pieces have larger surface area compared to their volume. After you cut the curds you will be cooking them before you drain. That's when whey will come out of the curds. They will get smaller over time. The bigger the pieces you start with and the bigger you can keep them by making sure they don't break apart when you stir, the more moisture they will hold when you drain and press them.
For curd size, milk quality is a very important piece of the puzzle. The fat in homogenized milk stops the rennet from working properly. This means that the milk doesn't have good "connection points" to stick together as a curd. It will "fracture" as you cook the curds and crumble into small pieces. You have to be *very* careful stirring curds with homogenized milk. I have some strategies that I use for homogenized milk, but generally I just try to avoid it, because it is very hard to work with.
The next place where you have control of moisture is in how hot you cook the curds, how vigorously you stir and how long you stir. The higher the temperature, when cooking the curds, the faster it will drain whey. As the curd is acidifying from the cultures, it will also drain whey faster. The longer you cook, and the higher the temperature, the more acidic the curds get and the more whey will drain. You must be careful, though. If your recipe asks you to raise the temperature (to dry out the curd, usually), it's easy to raise the temperature too quickly. If you do that, the outside of the curds will get dry while the inside stays wet. It will lock the moisture in the curd. This is called "case hardening". It is very important that you only raise the temperature by about 1 degree every 5-10 minutes. It's tricky and many people assume it doesn't matter (what difference does 1 degree make?) But it's an easy place to end up with too high moisture content (and usually too acidic a curd as a result).
And finally, the last place to control moisture content is how you drain and press it. When you remove the curds from the whey in the pot, that's called "draining". Usually you put the curds right into the mold. Some types of cheese drain on a board for a while first, though. The less acidic the curds are, the slower the whey will drain. This means that cheeses that have short cooking times and/or less starter culture and/or lower cooking temperatures will have more moisture than other cheeses. In my mind, the acidic of the cheese right out of the pot is almost the key for how your cheese is going to turn out later. Getting the moisture level in the curds and the acidic right at draining pretty much determines what kind of cheese you are making in many cases (which is amazing in its own right). It's subtle and tricky and requires lots of experience to get right. But with time you'll get a feel for how each type of cheese should react when you drain it.
When you press cheese, it's very important that it gets a chance to drain. Most people think that pressing is done to squeeze the whey out of the cheese. This is not correct. Whey will freely drain from the cheese even if you don't press it. It's true that pressing it will cause the whey to come out *faster*, but there is a problem. Just like cooking in the pot, if you press the cheese too hard, it will dry out on the outside. This will stop whey trapped n the inside from coming out. You always want to press with the *least* weight that you can. This will result in a cheese that has drained properly and will have the right texture.
Some recipes have weights for pressing. Just throw those numbers out of the window. They apply to the person to wrote the recipe. Your cheese and your setup is different. Also, most recipe authors seriously over press their cheeses in my experience (and you often see the defects in their final cheeses if they show them to you in a video or whatever). Also many recipes say to flip once over 2 or 3 hours. That's possible if you know how the cheese is going to react to the pressing, but you should never do that the first 4-5 times you make a specific cheese.
I usually put cheese in a mold and see if whey is draining at all. If it is, then there is no weight needed (this will be true of all but the driest cheeses). After 15 minutes flip and check how the curds are "closing" (making a smooth rind on the outside). You want the cheese to be fully closed after 2 hours, but *not* before. You only want enough weight in the press for whey to bead up in the holes. If it is running, then it is too much weight. Flip again after 15 minutes. From there you have 1.5 hours of draining left. Again put enough weight in the press for whey to bead up in the holes. Put more or less weight on depend on how fast it is closing. This time wait for 30 minutes. Do that 2 more times to get to 2 hours. At this point, the cheese should be fully closed (no marks on the outside of the rind). I usually remove the cloth in the last hour. For heavily pressed cheeses, I press lightly for a final 30-60 minutes just to erase any marks from the holes in the mold. Otherwise I'll let it sit in the mold with no weight so that it doesn't "slump" (squish out) as it's acidifying. When it hits the acidity target that I want (which I measure by tasting the whey that's draining out), I'll salt it.
So I'm sure that's way more information than you can process at once but those are the major points for controlling moisture in a cheese :-) It takes a *lot* of practice to get good at controlling it, but it's a fun hobby.
Last 2 questions: Thermophilic and mesophilic cultures contribute completely different flavors to the cheese. We choose the temperatures mainly for the culture that we want, not the other way around. In terms of subbing out thermophilic and mesophilic culture varieties, it *will* make a difference to the cheese. There are some major divisions in the cultures, though. Having a buttermilk culture as a mesophilic (something flora danica, or others that produce some gas) is pretty flexible for that side. On the thermophilic some cheeses really need something with "bulgaricus" in it and some need something with "helveticus" in it. The former is basically found in greek yogurt while the latter is something that is necessary for swiss or other alpine cheeses in that part of the world. However, if your goal is "cheese that tastes good", it doesn't matter what you use really. I make probably 90% of my cheeses with one (or both) of 2 cultures and I'm perfectly happy.
