More aesthetic norms, absolute values, parentheses, etc

This is nothing too important, and I’ve decided to make all three questions into one because they are more or less related. Sometimes when I type math equations, I find them not as beautiful as I thought they would be, and most of the time it’s because of symbols like () or | | of various sizes. Below are some examples:

1. When writing an exponent with parentheses inside a pair of parentheses, the most convenient way is to write f(x^{(n_1)}).
2. When writing a norm in which there are fractions and non-fractions, I’m using something like this: left| x - frac{x}{|x|} right|.
3. An operator acting on some kind of fraction: Tleft(frac{y}/{|y|}right).

The problems are (maybe it’s just me b/c this is really a subjective issue):

1. For the exponent, it’s just so unsatisfying to see that the ) outside is shorter and also wider than the one inside. I was able to roughly achieve what I want by using f scalebox{1}[1.2]{(}x^{(n_1)}scalebox{1}[1.2]{)}, but clearly doing so is much more time consuming.
2. This one makes me feel like the norm symbols are too large, and the first part (equivalent to Bigg| x looks especially weird. However, replacing them with Big| gives me something not large enough to cover the fractions inside.
3. This is just… weird — the letter T is so small compared with the left(, in this case Bigg(, and it looks a little bit disproportionate. Again, switching to bigg( bigg) gives me a pair of parenthesis that is not big enough to cover the fraction inside.
4. In text math fractions: with simply things I would do a / b, but when the fraction is more complicated, I either have to use frac{}{} or dfrac{}{}. With a complited fraction, the former is too small, whereas the second one sometimes look too big.

Maybe I was just being very weird, but I appreciate it if anyone can share any suggestion on how to make symbols like these more aesthetic (or maybe some methods, e.g., in preamble, to change the size of big, bigg ,and dfrac?).