And finally I'd like to address the third part of your question, if I understand it correctly: Why do the large chain rings in the front grow from the inside out (the outermost chain ring is the largest), while the little sprockets in the back cassette shrink (the outermost one is the smallest)?
The reason is that one tries to avoid running the chain "diagonally", that is, on the innermost chain ring in the front and the outermost in the back, and vice versa. In such a configuration, the chain must bend a lot because it runs "straight" (parallel to the bicycle) over the "sprockets" but at an angle from the front to the back. This quickly wears the teeth of the sprockets which take on the lateral force as well as the chain which works with the least friction when straight.
Since the highest gear results from using the largest front chain ring together with the smallest back sprocket, ordering the sprockets/chain rings the same way in the front and in the back would require the chain to run diagonally since the largest chain ring and the smallest sprocket would be opposed. The same is true in reverse for the smallest gear. These extreme gears would be unavailable for regular operation, and the adjacent gears would also need to be avoided for longer use.
Ordering the sprockets anti-parallel, by contrast, makes those extreme gears available with a straight chain, which is desirable. Shifting the chain both in the front and in the back in the same direction changes the transmission ratio; if the sprockets were ordered the same way, it wouldn't really change much because the ratio stays similar if you reduce (or increase) both the nominator and denominator at the same time. As depicted with the extremes, you'd need to increase "diagonality" of the chain in order to change the transmission ratio, which is undesirable.