Averb form which ends in -ing, -d, -ed, -n, -en, or -t, and is used as an adjective is called a(n)
appositive
gerund
infinitive
participle

PA verb form which ends in -ing, -d, -ed, -n, -en, or -t, and is used as an adjective is a called a PARTICIPLE.

A participle is a form of verb that is like an adjective where it modifies a noun, noun phrase, verb, or verb phrase. It is a type of nonfinite verb form.

Participles can be  present participles like writing, praising, and singing or they can be past participles like written, praised, and sung.

1. Cat and dog is proper noun cuz 'the' is used with both. It is being talked about the particular cat and dog, so it is proper noun. When they refer to a particular person or thing, then it is a proper noun. The park is also proper noun.

2. Misha - Proper noun

Plano - Proper noun

Drums - Proper noun

3. David - Proper noun

cake, cookies and cups - common noun

4. Danielle - Proper noun

Avatar - Pronoun noun

theather - it is the theater., so proper noun

5. Love - common noun

Peace - common noun

Hate - common noun

War - common noun

(P.S. - They are also abstract noun)

6. Family - common noun

7. Tom - Proper noun

banana - common noun

lunch - common noun

8. class - common noun

New York City - Proper noun

9. Movies - common noum

Frozen - proper noun