Is to be a special verb? As in, does it have a special sort of name? Because I feel it doesn't create direct objects like most verbs do. For instance, in a simple sentence: "I throw the ball." "I" is the subject, "throw" is the verb, and "the ball" receives the action, therefore it is the direct object. But using that same logic: "This is him." To most people this is grammatically correct, because it follows the same structure. "Is" is the verb, "him" receives the action, therefore you use a direct object pronoun. But actually, grammatically correct it should be "This is he." Is it because there is some reflexivity in using "to be?"
Well I search copula, it just says any word that links the subject to the predicate. Wouldn't that be most verbs? Jake throws the ball. "throws" links the subject to the object.
A copula semantically links the subject to the predicate, not just syntactically. This might not be a complete explanation, but the copula is used for categorical statements. Linking a subject to a predicate is like drawing a Venn diagram where the predicate is a circle and the subject is a circle inside the predicate. "The ball is blue" -- draw a circle representing blue objects. Draw a circle inside that circle. The inner circle represents the ball.
I think you are talking about two different things here, Rumwriter. "To be" is an infinitive. Infinitives can work as nouns, adjectives, or adverbs. An infinitive is not always preceded by "to" (aka the sign of an infinitive), sometimes the "to" is assumed, but it often is. An infinitive is the basic form of a word; the form you will find in the dictionary. There was debate on the properness of splitting infinitives (the most famous one being, "to boldly go where no man has gone before," where the "to" is separated from "go" by the adverb "boldly") but it has since been decided that there is no error in doing so. The only real problem with that iconic quote above is gender bias. The second issue you mentioned has to do with the pronoun's "case." There are three different cases: subjective, objective, and possessive. "This is he" is grammatically correct, and is in the subjective case, he being the subject of the phrase. It's the same as saying "here he is." You wouldn't say "here him is," (objective case) or "here his is" (possessive case). "He" is the only form of the word that makes sense. Pronoun case can be tricky to sort out. The most commonly mixed-up word with regards to pronoun case is the word "who." "Who" is in the subjective case, and is appropriate in the same situations as the words I, he, she, we, and they. "Whom" is in the objective case, and is appropriate in the same situations as me, him, her, us, and them. I'm not sure if this makes sense, but there you have it.
As already pointed out by @daemon, to be is a copular verb. English has just the one, but other languages can have more than one, hence the special name to describe this group of verbs. You are correct in that it does not set up a segue for a direct object. Copular verbs are intransitive and, again as already pointed out by @daemon, they are used to create categorical statements. Another difference is that unlike all other verbs, copular verbs are modified by adjectives or past participles (verb serving as adjective), and not by adverbs. I'm glad to see you're clearly digging through a well understood box of syntax and grammar tools, but no, what causes the oft used structure you mention is neither a reflexive nor even an ethical dative structure. It is merely something you already mentioned: the structure of the syntax feels to many like a direct object is being set up; thus, the pronoun is very commonly erroneously inflected into the accusative (also sometimes called objective) case. This is he is the correct syntax, but when spoken it's often appreciated as "over-correct" and stuffy. Hearing someone speak in that manner might make those who are sensitive to having their grammar corrected walk away from the conversation for fear that Officer Syntax O'Grammar is in their midst. The error doesn't obfuscate meaning and since the error is an application of the more predominant syntactic structure rather than something random, it persists, and in some speaking regions even supersedes the more formally correct structure. Failure to correctly set up the verb portion of subjunctive clauses is equally common for the same reason. There's enough surrounding syntax to hobble the clause along. *shrug*
