1. Little would have lived very happy in this good family if it had not been for the ill-natured cook.
(happy-> happily...right?)
2. The captain, who knew his business, took this opportunity to set forth the merits of Miss Puss. He told his majesty; "It is not very convenient to part with her, as, when she is gone, the rats and mice may destroy the goods in the ship?but to oblige your majesty, I will fetch her."
(Would you correct some errors,plese? What's the use of '?" after 'ship'?)
1. Yes, it should be "happily."
2. Comma after "majesty" not a semicolon.
There should be no question mark in #2 at all; however, that particular question mark is where you need to separate two sentences correctly. How will you do that?
Do we have to use ':' instead of '?'?
No, it'd be better to write it this way:
He told his majesty, "It is not very convenient to part with her, as, when she is gone, the rats and mice may destroy the goods in the ship. However, to oblige your majesty, I will fetch her."
1. Yes, you are correct. In the sentence "Little would have lived very happy in this good family if it had not been for the ill-natured cook," the word "happy" should be changed to "happily" to match the adverbial role that describes the verb "lived." The correct sentence would be: "Little would have lived very happily in this good family if it had not been for the ill-natured cook."
2. There are a couple of errors in the passage you provided. Firstly, the apostrophe in "captain, who knew his business" should be placed after the "s" in "captains" to show possession, making it "captain's." Secondly, the sentence "It is not very convenient to part with her, as, when she is gone, the rats and mice may destroy the goods in the ship?" has a misplaced question mark. The question mark should come after the word "ship" instead of before it. The corrected sentence would be: "It is not very convenient to part with her, as when she is gone, the rats and mice may destroy the goods in the ship. But to oblige your majesty, I will fetch her."