Our childhood experiences have made us what we are.
Us is the direct object.
What we are is the object complement. It complements or "completes" the direct object.
Yes, what we are is a noun phrase.
An object complement can be a noun, noun phrase, pronoun, or adjective.
Verbs such as make and create, and those such as name, call, and label often have object complements.
I named my daughter.
I named my daughter Alice.
The other students called April smart.
Josephine painted her elephant pink.
We elected Obama president.
The cats considered the dry food poison.
The witness called everything he saw a complete mess.
What distinguishes the direct object from the object complement?
The direct object takes the action of the verb. It comes before any object complement. To identify the direct object of a sentence, find the verb and ask "verb what?" or "verb who?" See this page.
Everything in bold is a direct object.
The object complement comes after the direct object. The words in italics are object complements.
Note that the order of words can change which noun is the direct object and which is the object complement. D.O. comes first.
I called my daughter Alice.
I called who?
I called my daughter. DO is my daughter.
Alice is OC.
I called Alice my daughter.
I called who?
I called Alice. DO is Alice.
my daughter is OC.
The city planners considered the plan amazing beyond belief.
Josephine found the homework she had done lying in the trash can.
Josephine found what?
the homework she had done is D.O. lying in the trash can is object complement.
Our childhood experiences have made us what we are.
Made who?
Made us (direct object)
what we are is object complement.
This page has more examples.
We can rephrase the sentence slightly, with emphasis:
The range of purposes that gongs are used for includes as a military signal, [as] a rhythmic accompaniment, and [as] a ritual instrument.
With this in mind, most of your questions become hard to parse, because include as isn't a coherent unit. I would just point out that you should not replace including with which include/s. This isn't because you can't do so, grammatically, but because it's not clear whether the verb should agree with (singular) range or (plural) purposes, and whichever you choose, nitpicking pedants will come out of the woodwork to correct you.
Best Answer
That [working at the desk] is an object complement, consisting of various grammatical elements. It's Jack who is [working at the desk].
working => Gerund-Participle form of verb, realised by a verb + ing. Here it indicates the action of Jack in progress at the time of my finding him.
at the desk => An adjunct, indicating the place where Jack's action is taking place at the time of my finding him. This adjunct is realised by a Prepositional Phrase (PP) - at the desk. The head preposition is - at and it's complement is a Noun Phrase (NP) - the (determiner) desk (head noun).