I am confused with "kind of".

"kind of" doesn't follow normal grammatical rules, it's a phrasal quantifier. It means the same thing as "somewhat"

Language rules are useful to learn the standard variety of language, but informal speech regularly breaks these rules and it's important to be conscious of that as well. By the way, there's no rule that only nouns can follow prepositions.

I often interpret ‘kinda(kind of) do’ as ‘somewhat do’. It’s common in speaking English, I guess.

Often, "kind of" is a set phrase meaning "somewhat" or "a little." For example, if something is "kind of true," then it might be true only in certain circumstances, or it might be a reasonable approximation of the truth (like how children learn approximations of complex scientific concepts). "Kind of" can also mean "in an unusual or unexpected way," as in, "that's kind of beautiful" referring to something that you wouldn't have thought of as beautiful on your own, but now that someone has pointed it out, you have to agree. This is totally separate from "kind of" as two distinct words, like "apples are a kind of fruit."

"Kind of" has turned into a phrasal adverb, meaning "somewhat". It is sometimes pronounced "kinda", and sometimes even written that way; it is functioning as a single word. I once tried to get myself to stop using it as an adverb, even in speech. I failed. It's kinda useful.

If “of” is actually being used as a preposition, then I agree it must be followed by a noun phrase. Here, though, “kind of” itself should be analyzed as an adverb phrase without any particular part of speech assigned to “of” itself. The usage derives (I think) from a transition from “X is a kind of Y” to “X is kind of Y”, where Y itself undergoes a shift in sense, from a noun to a verb or adjective.

What kind of confused? Very confused, or only kind of confused? I must say, it was very kind of all these people to explain it to you.

It took me quite some time to realize that there was languages first, then generalized rules. So if something widely used contradicts with the rules, just ignore the rules. Users of a language has the right of final interpretation.

"Kind of" is an adverb in that circumstance. It's not always a prepositional phrase.

This usage of “Kind of” is informal and should be thought of as a set phrase which is used as a single word, often informally written as kinda. It usually functions as a modifier for adjectives or an adverb, meaning somewhat or almost. Kinda heavy = somewhat heavy. Kind of blue = bluish, having a blue tinge. If he kinda jumped it means he almost jumped.

English is kind of confusing that way. You can have kinds of things, but they can be kind of similar.

It functions as a singular unit as an adverb.

It is kind of confusing. I also don't really like how it looks, which is why I use kinda

It's really functionally one word which is always an adjective or adverb. When I was a younger, I thought the word was "kinda" and it was one word as in "umm... that's kinda sus, broski" the "of" is pure etymological and not a genuine preposition in this context. You can also answer a question with the phrase too such as: "Do I look fat in this hazmut suit? Well, kinda..."

There is no such rule.

The play was kind of silly.  There's an example of an adjective after "of." Here's another one with a verb. The documents kind of took a while to arrive.  Perhaps play around with using verbs and adjectives after prepositions and get a feel for what sounds natural. This is a great place to cross check your discoveries! 

Don't think of it as a prepositional phrase. Think of it as an adverb that means "not fully"

What do you mean by "only nouns can follow behind prepositions"?