I do not believe that any of the sentences in this section tecnically contain "gerunds". " I am cooking chicken" is simply in the present progressive tense - which expresses currently ongoing action. "Cooking" used as a gerund would rather be "I like cooking" A gerund is a verb form used as a noun - in this case the object of "like"
You have to recall that this is a Spanish lesson. The gerundio in Spanish is a present participle describing a continuous action, and is translated (imperfectly) as "gerund".
Gerundio ≠ Gerund
A Gerundio is the Spanish Present Participle.
It cannot function as a noun. (In Spanish, all verbal nouns are infinitives.)
It can be used to form any of the Progressive Tenses and as an adverb.
An English Gerund is a verb ending in -ING functioning as a noun. Period.
In English, a verbal noun can be either a Gerund or an Infinitive.
English Present Participles can function as part of any Progressive Tense or an Adjective or a Noun.
Only when used as a noun is a Present Participle called a Gerund in English.