The way (that) he eats amuses me.
I found the way (that) leads out of here.
I love ice-cream in the same way (that) I love my mom.
1) The part of speech of the word that is conjunction in all three sentences?
2) Are all three parts in bold that-clauses/noun clauses? The second one seems to be missing a subject to qualify as a clause.
3) The parts in bold, are they appositives or complements? If the latter, are they subject or object complements?