Is the first sentence intended to contrast a particular type of welfare which has that quality with other types that do not? Or is it talking about the benefits of welfare in general? The second sentence is OK.
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Belinda ChenHe knows the singer (whom you think that her voice is wonderful.)This one needs help. He knows the singer whose voice you think is wonderful.
Belinda ChenThe man (who she assumed was bad) is actually a good guy.OK.
Belinda ChenHe is actor (who she thinksRemove "that he". You can't repeat a reference in your clause that is already used as the antecedent and the relative word. Here "actor" and "who" already refer to that sthat hewill win the prize.)
Belinda ChenFor the last one question: is the sentence below correct?The earthquake (which he predicted is coming will cause great damage.)Yes, it's fine (without the parentheses, of course).
Belinda ChenFor the first one, I would like to contrast a particular type of welfare.In that case I would recommend something like "It is the type of welfare which I believe can bring people a better life".