a) "some" quantifier and adjective (it does both)
b) "this__" demonstrative adjective (modifies a noun)
c) "__this" demonstrative pronoun (represents a noun)
2) He showed his father his sincerity by cooperating with all his teachers at school.
He = 3rd person subject pronoun
his = 3rd preson possessive adjective
by = preposition
cooperating = gerund (TEST: by his cooperating; gerunds take possessive adjectives)
all = adjective in form; substantive noun in function (TEST: all of his teachers)
showed = ditransitive verb, 3rd person singular, past tense
his father = indirect object
his sincerity = direct object
by cooperating with all his teachers at school = adverbial of manner
You're most welcome, Hela.