Of course I agree with Peachey, talking about english.
Coming to italian, the second item is wrong. The first one is slightly better.
The first part of the phrase is better in this way: "Il mio nipote più giovane non mangia mai gamberetti".
For the second part it all depends on how you complete the english phrase. If you say "He doesn't like them" you are referring to shrimps, so you must use the plural: "Non gli piacciono".
If you say "He doesn't like it" you are referring to the action (eating), so you can use the singular: "Non gli piace".