Jisho.org Forum

When ように(adv) or ような(adj) follows a noun, の should be used. When it follows an adj or verb, 連体形should be used.
For example,
雪のように(like snow). 雪is a noun
切れたように痛い (as painful as being cut). 切れたis a verb.
悲しいように(looking sad). 悲しい is a adj.
有用なように (seemingly useful). 有用なis the 連体形of 有用(Na-adj).

Similar rule also applies to うえ, うち, まま, はず, ため, etc.
For example

靴のまま入る (enter with shoes). 靴is a noun.
開けるまま (leaving open) 開けるis a verb.

Oh, I see now, even though it's still kinda hard for me to grasp...

Are ような and ように interchangeable?

And are the rules above the same for みたいに and みたいな?

ようなis an adj while ように is an adv.
Let's play some word game.

先生のような人が先生のように教えるようだ.
It seems that a person who looks like a teacher teaches like a teacher.

みたいis different. It follows a noun or a verb without の.

先生みたいな人が先生みたいに教えるみたいだ.

However, みたいis a word of colloquialism. In formal writing, you had better use ようinstead of みたい.

Or more simply: ~なNoun and ~にVerb

Nice grammar packed sentences ccpan. ^.^b