Feel confused about to-infinitive in a sentence

There are a number of different uses of infinitives;
one of them -- exemplified here -- is as a particular kind of Complement clause.

The answer to the first question is, Yes, the infinitive clauses can be considered the direct object of the verb (though not the infinitive -- that's just the verb in the clause; it's the clause that's acting like an object).

Incidentally, "to-infinitive" is not a useful term; most infinitives occur with to, and others don't, but they're all infinitives, and the presence or absence of to is determined by the context. To is not an intrinsic part of the infinitive, but is rather part of the ("For-To") Infinitive Complementizer. Requiring a special term for an infinitive with to is like requiring a special term for a woman wearing shoes; it's irrelevant, confusing, and unnecessary.

In the first cases, the sentence is parsed

• She never learned [(for her) to read (something)]
  and
• The goldfish need [(for the goldfish) to be fed (by someone)]
  -- which is derived via Passive from
• The goldfish need [(for someone) to feed the goldfish]

The bracketed parts are the direct object complement clause, with all the parenthesized parts -- indefinites and predictable subjects -- dropped, leaving only the infinitive behind.

Once you get clear that any verb appearing in a sentence is the verb of a separate clause and that every clause has a subject and a predicate, things clear up. That's the key to understanding the next question.

In the second case, it's quite wrong for the OALD to describe them as "Noun plus Infinitive". There are two quite distinct types represented here, and they have very different syntax.

I persuaded Sheila to chair the meeting is parsed

• I persuaded Sheila [(for Sheila) to chair the meeting]

whereas I expected her to pass the test is parsed

• I expected [(for) her to pass the test]

In the first case, the verb persuade has an Indirect Object (Sheila), as well as a Direct Object infinitive clause. This object complement clause (for Sheila to chair the meeting) has a subject (for Sheila), which gets deleted because it's identical to the Indirect Object.

In the second case, however, there is only a Direct Object clause (for her to pass the test), and so the subject can't be deleted by identity. In that case, only the subject complementizer for is deleted, leaving her in subject position in the infinitive clause.

Which also happens to be object position in the main clause -- isn't English syntax fun? (I might add that there is a lot more detail and complexity here.

A. Yes, you can think of those infinitives as objects; they serve a very similar function, even though infinitives are normally not so called.

B. "Why" is a difficult question. That's just the way it is. It is a special construction. You may want to read up on raising.

C. Persuade Sheila to chair is indeed similar, but still somewhat different. You can say I persuaded Sheila, and adding to chair the meeting doesn't change the meaning of the verb; however, in I'd love you to come, you can say I'd love you, but then love has a different meaning. That's the difference. The addition of the infinitive changes more than just the additional information. You could say the infinitive is more like a syntactical complement in the love sentence than in the persuade sentence.