All are correct.
The only change would be in the first sentence. Substitute "asked" for "said."
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?)
2 answers
One other fairly minor thing -- you need to delete the comma in #1.
1 answer