I can't draw the actual tree here, but I can help you identify the parts of speech in the above sentences which may help you then create the tree in the appropriate manner. The words of the actual sentence are in bold.
1. The (article) modifies principal (subject of indepedent clause), said is the verb. That is a relative pronoun that is introducing the rest of the sentence which is a dependent clause. In that-clause: the (article) modifies school (subject) closes (verb) for (preposition) the (article) day (object of the preposition). The whole dependent clause is functioning as a direct object of the independent clause.
2. The (article) boy (subject) is (linking verb) eating (gerund, complement of subject).
3. The (article) man (subject) with (preposition) the (article) hat (object of the preposition) smiled (verb).
4. The (article) boy (subject) who (relative pronoun subject of the dependent clause) was (linking verb) sleeping (gerund, complement of who) was (linking verb of main clause) dreaming (gerund, complement of boy).
5. The (article) guy (subject of independent clause) we (subject of dependent clause) met (verb of dependent clause) at (preposition) the (article) party (object of preposition) next door (adj-noun post-modifiers of noun party) seems (linking main verb of main clause) cute (adjective, complement of subject guy).