(1) I have checked my books, and I believe the following to be
(2) First, "He tends to be unhappy" is NOT the same as so-called
"complementary infinitives": I have to go; I am going to study; I used
to work there. As Descriptive English Grammar points out, those
three sentences could be expressed as: I must go; I shall study; I once
worked there. It is my opinion that "He tends to be unhappy" does not
fit that pattern.
(3) Yes, you are 100% correct. We could say that in "I agree to leave,"
"to leave" is the direct object of the verb "agree." Here's another
example from Descriptive English Grammar: He helps (to) support his
(4) Re: "He tends to be unhappy," both Descriptive English Grammar
and A Comprehensive Grammar of the English Language point out that
"tend to" is similar to "seem to."
In other words, the infinitive "to be unhappy" has the function of an
adjective. It is a subjective complement. Obviously, you cannot say:
He tends. You need a complement (the word "complement" comes from
the word "complete") to complete the meaning of the sentence. Thus, we
can probably conclude that the infinitive phrase "to be unhappy" is a
subjective complement -- NOT an object.