Question

1. I agree with you that watching TV is a waste of time.

2. I agree with you about the statement that watching TV is a waste of time.

3. I agree that watching TV is a waste of time.
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Q1: Are they all grammatical? Do they have the same meaning?

Q2: What is the part of speech of 'that' in Sentence 3? Is "the that clause" an adverbial clause in #3?

Answer 1

All 3 mean about the same thing, although #2 is wordy.

The word "that" in #s 1 and 3 is a subordinating conjunction except it's introducing a phrase instead of a clause.
http://grammar.ccc.commnet.edu/grammar/conjunctions.htm#subordinating_conjunctions