Both sentences are essentially identical in meaning. Keep in mind, the first is really 'he thinks this IS important'. If 'is' is omitted, it is strongly implied. Both can equally mean 'He is an idiot ....." if you chose to give this meaning by the tone, intonation or pitch of your voice.

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Yes, "he thinks this important" has the same meaning. Grammatically, you do not need the word "is," but note that the construction without "is" sounds very old-fashioned. You would be unlikely to hear anyone say it this way in modern speech (and if you say it this way yourself, some people will assume you're making a mistake). You may, however, encounter sentences like "he thinks this important" in older books, or in fantasy films or historical films where the characters are using slightly archaic English.

Yes they both convey basically the same meaning. If you said either of them you would be understood in the same way. But I think you missed “is” in the first example. “He thinks this important” doesn’t really make sense. It should be “he thinks this is important”