I forgot to include the following two alternatives. Thank you very much for your cooperation.
1)"Shall I get a candle?", he said. He wondered whether he should get a candle.
He wanted to know if he should get a candle.
2)He asked me if I would like to have lunch with him on that Sunday.
3) She suggested having a party. (Is the gerund in this sentence wrong?)
All are correct.
The only change would be in the first sentence. Substitute "asked" for "said."
One other fairly minor thing -- you need to delete the comma in #1.
1) "Shall I get a candle?", he said. He wondered whether he should get a candle.
He wanted to know if he should get a candle.
To rewrite this sentence, you can convert the reported speech into direct speech. Here's how:
Original sentence: "Shall I get a candle?", he said.
Direct speech: He said, "Shall I get a candle?"
Question form: Should I get a candle?
Rephrased sentence: He wondered if he should get a candle.
2) He asked me if I would like to have lunch with him on that Sunday.
This sentence is already correctly written. It is a reported speech where someone is asking about the possibility of having lunch together on a specific day. No revisions are necessary here.
3) She suggested having a party. (Is the gerund in this sentence wrong?)
No, the gerund in this sentence is not wrong. The phrase "having a party" functions as a noun and follows the verb "suggested." The gerund form of the verb "have" is appropriate here since it is used as the object of the verb "suggested." Thus, the sentence is grammatically correct.