***** NOT A TEACHER *****
(1) Yes, English is, indeed, "difficult and confusing." Of course,
I guess all languages are difficult and confusing.
(2) I do not believe that "have no idea" qualifies as a
phrasal verb. Here are some "real" phrasal verbs that I found
mentioned in The Oxford Dictionary of English Grammar:
The plane took off./ I don't know -- I give up!/ Take off your coat.
(3) Your last question is really interesting. I discovered (for the
first time) that there are many grammatical theories regarding
a sentence such as:
"I have no idea where Tom has gone."
Those ideas are too difficult for me to understand. (Yes, you are right!!!
Some experts feel that "where Tom has gone" is some kind of direct
object in that sentence. That is too difficult for me to understand.
Some scholars see "where Tom has gone" as playing some kind of
adverbial role. Again I do not understand.)
The simplest explanation given by many experts (and the only idea
that I can understand) is that "where Tom has gone" is the object
of some suppressed (deleted/omitted) preposition. For example, one
scholarly book gives this:
I have no idea about why he hasn't shown up.
(These ideas come from a Google book entitled Wh-clause in English:
aspects of theory and description by Mr. Joe Trotta.)
(4) Like you, I am eager to see what the teachers (and knowledgeable
non-teachers) have to say.