I think muscle fiber typing are a little overrated. First, no one really know their muscle fiber types anyways. And second, it's not just fast twitch or slow twitch. Humans try to put things in nice, neat categories, but that's not really how it works. For instance, in this article, they mention 5 different muscle fiber types and say "the fiber type profile of human skeletal muscle has now been shown to have a high degree of plasticity, with a primary regulator of fiber type alterations being physical activity".
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3358799/
So basically, there's a bunch of different types, muscle fibers can change with training, and you don't know your muscle types anyways.
With mitochondria and capillary density, first think about the body as a whole. So when you are running you need ATP in able for a muscle contraction to them act on a joining (causing you to move). You can make ATP using the creatine phosphate system (but only ~5-8 seconds worth and this is partly why strength athletes take creatine) anaerobic glycolysis (without oxygen which produces lactate and Hydrogen ions that make your legs burn) and aerobic respiration. Obviously aerobic respiration is the major factor to improve distance running.
So how do we get oxygen to the muscles and ultimately convert it to ATP.
First, we need to actually deliver oxygen to the muscle. So pulmonary exchange takes place in the lungs (your bloods gets rid of CO2 and picks up O2), then the heart has to push the blood out. How much blood your heart pushes out is called Cardiac Output (CO). CO= Stroke Volume (how much blood your heart can pump per second) X Heart Rate. Max Heart Rate doesn't change a whole lot, the the primary change is Stroke Volume. Your left ventricle of the heart gets strong and can push out more blood. Some studies say that and increase in stoke volume can be stimulated at intensities as low as 40% VO2 max (pretty low), but other research has shown the stimulus for increased stroke volume increases a little bit more linearly with intensity. Regardless, this is a big reason why easy running is so beneficial for new runners because stroke volume increases.
In order for your blood to carry oxygen, it needs red blood cells with hemoglobin (and iron is in hemoglobin to transport oxygen which is why you need it). EPO simulates the production of red blood cells which is why people dope with it. Training can lead to increased red blood cells. There are some other factors in blood and blood vessels such as plasma volume and vasodilation/vasoconstriction. For example vasodilation widens the blood vessels to enhance blood flow. Nitric Oxide can stimulate vasodilation which is why people eat nitrate-rich foods like beet juice, spinach and arugula.
So once your blood carries the oxygen, it has to get rid of it and actually delivery it to the muscle. So think of the main artery as a highway- when the blood reaches its destination is gets off the highway and exits into the capillaries. There- just like a mailman, it drops off oxygen, and picks up carbon dioxide.
So everything above was the oxygen delivery system- getting the oxygen to your muscles. Now, your muscles have to be able to use it. Your muscles have myoglobin (this is similar to hemoglobin, but in your muscle). Myoglobin facilitates oxygen diffusion and stores oxygen in the muscle. The more myoglobin you have, the more oxygen you can get into the muscle. (Note: myoglobin has a reddish color, this is why the 'slow-twitch' oxidative muscles are the red ones... but again muscle-fiber types aren't that simple).
Once you have oxygen in the muscle, you need mitochondria. This is where aerobic respiration takes place. So the more mitochondria you have, the more oxygen you can utilize. Not only can you make more mitochondria, but you can actually improve the quality of the mitochondria (so they work faster).
These are the basics. I used to research exactly what training methods produces specific changes in these different parameters such as " what type of workout will help me increase more mitochondria?" But I've found that's not really a great approach because that's not how real world training works. Basically, if you gradually increase mileage with some relatively easy running, include some longer runs of 75-90 mins, and have some bouts of high intensity, you're going to increase all of these- assuming you recover well and have adequate nutrition such as enough iron.
Next I would explore lactate threshold and the dynamics of how lactate and hydrogen ions form, how they are buffered, and how they get removed from the muscle cells and ultimately recycled in your body.