What is the subject,object and verb in these questions sentences? "When does one become an angel?" "Who must have spoken eloquently?

I think that the previous poster did a good job explaining how to go about answering your question, with a detailed step-by-step process, but I'm not sure that one of the answers (and the process that produced the answer) is entirely correct.

The sentence "When does one become an angel?" does not have a direct object. It has a predicate noun, instead.

It is indeed a good idea to first move the adverb to the end of the sentence: "One does become an angel when." However, simply asking now "who" or "what" won't distinguish direct objects from predicate nouns. One clear distinction between the two is that a direct object is very different from the subject whereas predicate noun renames or redescribes the subject.

One = the subject

does become = the verb (it's a linking verb)

an angel = the predicate noun

"One" and "an angel" are much too similar to be subject and direct object. Also, I believe that "become" is always (or at least almost always) a linking verb.

Here are some more examples:

I like you. = "you" is the direct object

I like myself. = "myself" is the predicate noun (or, more precisely, a reflexive pronoun functioning as a predicate noun)

She drives a Mercedes. = "Mercedes" is a direct object.

The car is a Mercedes. = "Mercedes" is a predicate noun

Even supposedly simple grammar can be tricky to do and even trickier to explain. I teach this stuff, too, and correct myself in the middle of class all the time.