Question

Thank you for your help.

1. Monday is the day when I am the busiest.

2. Monday is the day when I am busiest.

3. Monday is the day I am the busiest.

4. Monday is when I am the busiest.

5. Monday is the day that I am the busiest.

6. Monday is that I am the busiest.
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Q1: Are they all grammatical?
Q2: Do we have to put 'the' before 'busiest' in this sentence?
Q3:In Sentence 4, 'the day' is omitted. In this case, what is the part of speech of 'when'? An interrogative adverb or a relative adverb?

Answer 1

1 - 5 are fine. 6 is not.

Adding the word "the" seems to just provide emphasis, but doesn't change the meaning.

In 4, "when" is the interrogative that is introducing the indirect question. It's not a relative-anything.

Interrogatives: when, where, who, whether, how ... http://grammar.ccc.commnet.edu/grammar/marks/question.htm#indirect and http://www.perfect-english-grammar.com/indirect-questions.html

Relative pronouns introduce relative clauses -- http://www.chompchomp.com/terms/relativeclause.htm -- and some relative pronouns also serve as interrogatives.