This "buried" is the so-called past participle. The past participle is a non-finite verb form. The other non-finite forms are the infinitive and the gerund. "Non-finite" means something like unbounded. There are two characteristics common to non-finite forms in English. They are not bound to a subject. They are not bound by time. Another way to express the same idea is to say that they do not form predicates and they do not have tense.
1) Is this "buried" an adjective? No, not really. It's a participle. It is derived from a base verb.
Past participles express some result of the verbs from which they are formed. For action verbs like "to bury", they represent a state that results from the action. If I bury a treasure, the result is a buried treasure. If I bury a treasure in my back yard, the result is a treasure buried in my back yard.
So, we start with the fact that participles can modify nouns in much the same way that adjectives can. Even though "buried" is a verb and "happy" is an adjective, we can see the same grammatical relationships in "a buried treasure" and "a happy man".
When a participle modifies a noun in the manner of an adjective, it seems reasonable to call it "an adjective participle" or "a participial adjective". Those are nothing but shorthand for "a participle doing an adjective's job".
2) Is this "buried" a participial adjective? Sure, why not?
The argument of a copular (or linking) verb isn't called an object; it's called a complement. Specifically, it's a subject (or subjective) complement. There are two kinds of subject complements. One kind is a different reference for the same referent, or a restatement of the subject. We call that kind "nominative". In the sentence "he is our teacher," "our teacher" is the predicate nominative subject complement. The other kind of subject complement modifies the subject. We call this kind "adjective". In the sentence "he is happy", "happy" is the predicate adjective subject complement.
In the sentence "he is buried", we can see that "buried" still does the same job as an adjective like "happy". We can call it a participial adjective serving as the predicate adjective subject complement.
3) Is this "buried" a predicate nominative? No, it's a predicate adjective.
Even though the past participle "buried" doesn't take a subject, it is still a form of an action verb. It implies an actor or agent.
This is the basis of passive-voice constructions. This is the reason that passive-voice constructions exist and make sense.
The sentence "he is buried" implies at least one of the following: Someone or something buries him. Someone or something buried him. Someone or something has buried him. Since the participle "buried" has no tense, the grammar of "he is buried" cannot tell us the time of the act of burying.
There is no conflict between interpreting "is buried" as the copula with a participial predicate adjective subject complement and interpreting it as the passive voice, present tense, indefinite aspect and indicative mode construction. The latter interpretation makes sense because the former interpretation carries the same semantics. Those two interpretations result in the same meaning.
4) Is the clause in the passive voice? Yep.
5) Does “he is buried” mean currently his body lies in a coffin covered with soil, or does it mean he has been buried by someone?
This "or" doesn't make sense to me. If he is buried, if his present-tense state is the result of the action of burying, then some actor or agent for the action of burying is implied. From the grammar alone, I can't tell whether the indefinite aspect represents a habitual state (i.e. he is usually buried because someone/thing often buries him) or merely a current state (e.g. he is now buried because someone/thing buried him earlier). The mechanisms for knowing which of these possibilities makes sense in a given context is called pragmatics.
If we say "he was buried", that clearly references a state that existed in the past, and it can suggest that the state has ended or changed. Obviously, it doesn't require that the state has changed. A sentence like "He was buried there yesterday, so I assume he's still there" makes as much sense as "He was buried there, and I have no idea where he is now."