I have did the corrections for my english homework I posted a few days ago. Can someone check it over again and give me some suggestion if they are still wrong. Thank you!!

Identify the phrase in the sentence below, and name the kind and function of each phrase.

a)Having had a good season, they hoped to win the trophy.
having had a good season: adjectival participial phrase
to win the trophy: infinitival noun phrase, direct object

b)In the last few weeks, they have often been seen going to the theatre together.
In the last few weeks : adverbial prepositional phrase
going to the theatre together: adjectival participial phrase

c)The car parked in the garage is not for rent
parked in the garage: adjectival participial phrase
for rent: adverbial prepositional phrase

d)Rejecting their offer, she said she was no longer interested in doing business with them
Rejecting their offer: adverbial participial phrase
doing business: gerund, subject complement
with them: adverbial prepositional phrase

e)To be honest, I don’t want to take extra work at the moment
to be honest: infinitival adverb phrase
to take extra work: infinitival noun phrase, direct object
at the moment: adjectival prepositional phrase

f)Eating and Drinking was forbidden during the performance.
Eating and Drinking: gerund, subject
during the performance: adjectival prepositional phrase

g)During the good weather, it is hard to stay indoors and study
During the good weather: adjectival prepositional phrase
to stay indoors and study: : infinitival extraposed noun phrase subject

h)Bored with the game, he walked to the exit whistling loudly
Bored with the game: adverbial participial phrase
whistling loudly: adjectival participial phrase

i)If it continues to rain like this, we will have to leave
If it continues: adverbial prepositional phrase
to rain like this: infinitival noun phrase, direct object
to leave: infinitival noun phrase, direct object

j)The way to lose weight is to exercise a lot.
to lose weight: infinitival adjective phrase, direct object
to exercise a lot: infinitival noun phrase, subject complement

2 answers

a)Having had a good season, they hoped to win the trophy.
having had a good season: adjectival participial phrase right
to win the trophy: infinitival noun phrase, direct object right

b)In the last few weeks, they have often been seen going to the theatre together.
In the last few weeks : adverbial prepositional phrase right
going to the theatre together: adjectival participial phrase right

c)The car parked in the garage is not for rent
parked in the garage: adjectival participial phrase right
for rent: adverbial prepositional phrase It's a prepositional phrase, all right, but I'm not sure about "adverbial."

d)Rejecting their offer, she said she was no longer interested in doing business with them
Rejecting their offer: adverbial participial phrase right
doing business: gerund, subject complement gerund, yes; but you'll need to explain the rest to me
with them: adverbial prepositional phrase right

e)To be honest, I don’t want to take extra work at the moment
to be honest: infinitival adverb phrase right
to take extra work: infinitival noun phrase, direct object right
at the moment: adjectival prepositional phrase prepositional phrase, yes; please explain how it's adverbial

f)Eating and Drinking was forbidden during the performance.
Eating and Drinking: gerund, subject right
during the performance: adjectival prepositional phrase right

g)During the good weather, it is hard to stay indoors and study
During the good weather: adjectival prepositional phrase right
to stay indoors and study: infinitival extraposed noun phrase subject right

h)Bored with the game, he walked to the exit whistling loudly
Bored with the game: adverbial participial phrase right
whistling loudly: adjectival participial phrase right

i)If it continues to rain like this, we will have to leave
If it continues: adverbial prepositional phrase adverbial, yes; but not a prepositional phrase
to rain like this: infinitival noun phrase, direct object right
to leave: infinitival noun phrase, direct object right, I think

j)The way to lose weight is to exercise a lot.
to lose weight: infinitival adjective phrase, direct object no adjective (word or phrase) will be a direct object
to exercise a lot: infinitival noun phrase, subject complement right
fool