1. I knew when he would come back.

(What is the part of speech of 'when' in the sentence? Is it an interrogative adverb or a relative pronoun?)

2. I knew the time when he would come back.

(In this sentence 'when' is a relative pronoun, right?)

3. I know ___? + When will he come back?

--> I know when he will come back.

(If the two expressions are combined and make the sentence, 'when' can be regarded as an interrogative adverb. Right?)

4. I know the time when he will come.
(In this sentence, 'when' will be omitted. Then 'when' can be regarded as a relative adverb, right? as in the sentence" I know when he will come.)

1. The word "when" is a subordinating conjunction. It introduces the subordinate clause ("when he would come back"). [The main clause is "I knew."]

http://grammar.ccc.commnet.edu/grammar/conjunctions.htm#subordinating_conjunctions

2. Yes. It introduces the clause "when he would come back" which is serving as an adjective -- the whole clause modifies the word "time."
http://owl.english.purdue.edu/owl/resource/645/01/

3. No -- see #1 above.

4. See #2 above. It's the same construction even though the words are slightly different.

1. In the sentence, "I knew when he would come back," the word 'when' is not an interrogative adverb or a relative pronoun. It is actually a subordinating conjunction. It introduces a subordinate clause that modifies the verb 'knew' and indicates the time at which the action of the main clause took place.

2. In the sentence, "I knew the time when he would come back," 'when' functions as a relative pronoun. It introduces a relative clause that describes or identifies the noun 'time'. This relative clause provides additional information about the time at which the person would come back.

3. In the sentence, "I know when he will come back," 'when' is still a subordinating conjunction. It introduces a subordinate clause that functions as the direct object of the verb 'know'. The clause answers the question "When will he come back?" and provides the information that the speaker knows.

4. In the sentence, "I know the time when he will come," 'when' can indeed be omitted without changing the meaning. In this case, 'when' is acting as a relative adverb. It introduces a relative clause that modifies the noun 'time'. This clause provides additional information about the time of the person's arrival. However, it is important to note that the word 'when' is frequently used in this context but can be omitted in situations where the meaning is clear without it.