'To keep' acts as an adjective modifying 'promise'. It is an infinitive.

Here, 'reading' describes the purpose of the lamp (a lamp *for* reading), not that the lamp itself is reading. It is a gerund used as a noun adjunct.

'Reading' acts as the head of the subject phrase. It is a gerund (verbal noun).

Here, 'so' replaces a clause (e.g., 'that it is true'). It functions as a pronoun (specifically a pro-form substitute).

'So' modifies the adjective 'cold', indicating degree. It is an adverb.

'Err' is a verb. 'To err' is the infinitive form functioning as the subject of the sentence.

Here, 'while' is the object of the preposition 'For' and is preceded by 'a', referring to a period of time. It is a noun.

'While' connects two clauses ('Sit' and 'I read') indicating simultaneous action. It is a conjunction.

It follows a linking verb 'is' and describes the subject. It is a predicate adjective.

It appears directly before the noun 'nut', making it an attributive adjective.