1. Here is a man who wants to see you.

2. Here is a man wants to see you.

3. There are two boys who want to play tennis.

4. There are two boys want to play tennis.

(Can we omit 'who' as in #2 and #4? Are they all correct?)

no you cannot take out the who in any sentence. Read them out loud to your self. The second ones just do not sound correct and that is because they are not. Proper English will keep who in both sentences.

Anonymous is correct. The word "who" is necessary because it's the subject of the word "want(s)."

In these sentences, the use of "who" is necessary for correct grammar and clear meaning. Let's analyze each sentence to understand why.

1. Here is a man who wants to see you.
In this sentence, the use of "who" is correct because it introduces a relative clause describing the man. The relative clause "who wants to see you" helps provide additional information about the man's desire to see you.

2. Here is a man wants to see you.
This sentence is not grammatically correct. Without the relative pronoun "who," the sentence lacks a subject for the verb "wants." The correct version would be the first sentence, where "who" introduces the relative clause.

3. There are two boys who want to play tennis.
Using "who" in this sentence is necessary to introduce the relative clause describing the boys. The clause "who want to play tennis" provides information about the boys' desire to play tennis.

4. There are two boys want to play tennis.
Similar to sentence #2, this sentence is not grammatically correct. Without "who," there is no subject for the verb "want." The correct version would include the relative pronoun "who" to introduce the relative clause, as shown in sentence #3.

In summary, the correct sentences are sentences #1 and #3 because they use the relative pronoun "who" to introduce the relative clauses. The sentences without "who" (sentences #2 and #4) are grammatically incorrect and should be modified to include the relative pronoun.