Is ように solely for verbs while のような for nouns? What about adjectives?
I think it is best if you just treat 様【よう】 as a normal noun. With other nouns, you should be using のよう because that is how nouns modify each other. With na-adjs, you should be using なよう because that is how they modify nouns. And so on. So:
Like a student
as you like
In a nice way
For whether you should be using ような or ように, the same applies. な used by な-adj to describe a noun while に is used to make it an adverb. For example, きれいに makes it an adverb while きれいな is an adjective. In the same way, ような makes it an adj while ように makes it an adverb. This means choosing between the two depends on what よう is modifying.
Study like a student.
A uniform like a student's.
Adverbs, much like in English, can also modify adjectives, so you would use ように
Nice like him
I had the same issue of understanding this as well. As per my understanding adverb are words like honto ni, zettai, totemo, hayaku eg. are used to add more description to a verb or noun.
Chichi no you na otona ni naritai desu. (When I grow up I want to be someone like my father)
Ningyo no you na kao desu. (Face which is similar to a doll's)
How about this example :
Sentaku mondai no you ni tesuto ga ii desu Vs sentaku mondai no you na tesuto ga ii desu.