relative clause and pronoun , object and complement

Question

I learned that in relative clauses, the relative pronoun acts as a subject or an object or a complement.

Red is the color which we painted the wall.

Is this sentence grammatical?
Paint is a verb that should be followed by a object and a complement, so I think red act as a complement in this relative clause, therefore the sentence should make sense. Is that right?

The teacher doesn't like the student whom we elected class president.

Elected is a verb that should be followed by two objects, so in this clause, even though we have one object class president already, one object is still missing , and whom represents the missing object, is that right?

This is a lesson which the students are eager to learn.

I am slightly confused with this one, inside the relative clause
Subject : the students , verb : are , complement(adj) : eager
to learn acts as an adverb to modfiy the complement(adj) eager,
so the clause itself seems complete already, so what does the relative pronoun which represents here ?

Answer 1

Which points to the complement (more precisely, the direct object) of to learn: The students are eager to learn [this lesson]. To learn [this lesson] is the complement of the adjective eager.

(Yes, adjectives have complements too!)

Here's a tree diagram which illustrates the complexity of the structure:

Which refers backward to a lesson and forward to the missing object of learn. Students is the implicit subject of the infinitival clause which is the complement of the adjective eager.