I am sorry to say that in English we do not normally use either of the sentences you put forward. 1. "I don't like what she likes" means "I dislike everything that she likes." It is very childish, or hostile, or both. For that reason, we do not normally say it. You could say "I don't like France", "I don't like chicken" or "She and I don't always have the same taste." 2. In English, we say "I'll have the same" or "I'll have the same as he", or "I'll have what he is having".

“I xxx what he yyy？” means that “我xxx他yyy的。” "I don't like what she likes" means that “我不喜欢她喜欢的。” “I will have what he has” means that “我想吃他吃的。” in fact, we will not say like that. but if a foreigner say that, most chinese will got it.

We usually say 我喜欢的和他不一样。 我要和他一样的。