Answer:
Denny and I love to ride our bikes around the park.
I is used when the person narrating is the subject of the sentence i.e. are the ones performing an action. As both Denny and the narrator are performing the act, they are both subjects and I should be used.
Both of us are planning to watch a superhero movie on Sunday.
Use the pronoun us when Both of has been written because it will then show that the action is being undertaken by the 2 people.
We can't go the pool now because they have closed.
Use they when referring to a noun that is the subject of the sentence in plural. The subject here would be the pool owners who would have closed.