3) We have to put the powder in it. (for the verb 'have to put' is it a modal, auxiliary and verb?)
HAVE: full verb
(TO) PUT: dependent infinitive
There is no modal verb here.
5) Cause I'm very good at going under the table. (would 'at going under the table' be an adverbial subordinate clause?)
No, it is an adverbial prepositional phrase.
6) Now would you like something to eat? (what would the 'like' be? is it a verb?)
7) We are doing something special. (would 'special' be an adjective?)
9) Maybe the puppet just pulled it. (what would 'maybe' be?)
10) The one that didn't want to come out of his box. (would it be an adverbial subordinate clause from 'that'>)
No, a relative clause.
(N.B. This is not a complete sentence!)
11) Just wait! (would it be adverb and verb?)