The sentence
1. The child laughed merrily.
It is a simple, two-member, complete sentence. It is extended. According to the communicative type the sentence is declarative.
2. English spring flowers!
It is a simple, one-member, nominal sentence. It is extended. According to the communicative type the sentence is exclamatory.
3. “Where are you going?” ― “To the library”.
“Where are you going?” is a simple, two-member, complete, extended sentence. According to the communicative type, the sentence is interrogative. It is a special question.
“To the library” is a simple, two-member, elliptical sentence. The subject and the predicate are omitted. The sentence is extended.
The subject
Two thousand passengers were believed to be injured.
Two thousand passengers is phrasal subject, expressed by a phrase with a numeral.
To understand is to forgive.
To understand is a simple subject, expressed by an Infinitive.
Your doing this is very strange.
Your doing this is a complex subject, expressed by a gerundial construction.
What he expected began.
What he expected is a clausal subject.
The object
Meet her tomorrow.
Her is a simple object, expressed by a personal pronoun.
I saw a strange man there.
A strange man is a phrasal object, expressed by a nominal phrase.
She remembered meeting her last year.
Meeting her is a phrasal object, expressed by a gerundial phrase.
I want to have my photo taken.
My photo taken is a complex object, expressed by a construction with Participle II.
He insisted on my telling the truth.
My telling is a complex object, expressed by a Gerundial construction.
I want him to stay.
Him to stay is a complex object, expressed by an Infinitive construction.
Ron was amazed by what he saw there.
What he saw there is a clausal object.
The attribute
There were no signs of his supporting us.
Of his supporting us is a complex postmodifying attribute. It is expressed by a gerundial construction.
She is a clever girl.
Clever is a simple premodifying attribute. It’s expressed by an adjective.
The adverbial modifier
John lives in London.
In London is a simple adverbial modifier of place, non-detached.
Despite his smile, the man was difficult to deal with.
Despite his smile is a phrasal adverbial modifier of concession, detached.
It being late, he left the garden.
It being late is a complex detached adverbial modifier of reason, it is expressed by the Nominative Absolute Construction with Participle I.
The composite sentence The Compound Sentence
You can join us at the station, or we can wait for you at home.
It is a compound sentence consisting of two clauses. The clauses are joined by means of disjunctive coordination with the help of the conjunction ‘or’.
The bus stopped, the automatic door sprang open, a lady got in.
It is a compound sentence consisting of three clauses. The clauses are joined asyndetically.