Great questions! Here are my thoughts
"I am wondering why we are identifying our body types? Is it to dress the parts you like to accentuate them and de-emphasize the other parts you don't like?"
I wouldn't say it's to de-emphasize parts we don't like; for example, I have a strong shoulder line so I have to be mindful of that so I don't end up looking crazy broad in the shoulder, but I certainly love my shoulders! Once you know your body type, you have a set of guidelines to help you in determining which clothing cuts will make you look your best, but they are just guidelines.
"I am confused about what balance means also, when it comes to clothing and dressing."
Balance can mean many things, and different people look for different types of balance. It could be balancing narrow hips against wide shoulders, a large bust, a long torso with short legs, a long neck, etc. Balance can also refer to balance of styles, such as pairing a tough element with an otherwise girly outfit. And balance can also refer to the "weight" within a single outfit, such as ensuring that the top half of your outfit doesn't look heavier than the bottom half. Most of our dressing will involve several types of balance at once, even if we're not fully conscious that we're doing so.
"Also, how do we combine what our body type guidelines are suggesting we should wear and the MOTG outfits - for example wearing a cropped cardi or flyaway cardi- what if your body type guidelines say that won't flatter your body?"
The MOTG formulas show examples, but you certainly don't have to follow the examples exactly. So for the formula Jeans + embellished / graphic T + new look cardigan + ballet flats, you would pick the jeans silhouette flatters most, a tee with the neckline and sleeve that's most flattering, a cardigan in a style that's flattering, and flats. For one person this could mean skinnies, a sparkly cap-sleeve tee, a cascading cardigan, and flats. And for someone else this could mean straight leg jeans, a deep v-neck tee with 3/4 sleeves, a cropped cardigan, and flats.