As an American, we shorten "are" to /ər/ in fast spoken pronunciation.
But usually only if the final sound of the word before the "are" is a consonant sound.
I would pronounce these two sentences the same, if speaking quickly:
Problems of most people are not big. => Problems of most peopler not big.
Notice how the "are" seems to attach itself to the end of the previous word. That flows easily pronunciation-wise in your examples 2 and 3 as well.
People who smoke cigarettes are gross => People who smoke cigaretteser gross
People who smoke are gross => People who smoker gross
However, it doesn't flow as naturally and easily with your last example because the word before ends with a vowel sound, making it hard to attach the "are" as /ər/. If I try to say /ər/ after "me", I am forced to make it its own syllable, and since "are" should be pronounced /ar/, then that is how it gets pronounced in that sentence. It ends up taking more energy to force it to be pronounced as /ər/ in that situation.
People who hate me are deluded.
(Note: The words "peopler", "cigaretteser", and "smoker" in the examples are meant only to show pronunciation, and are not examples of proper spelling or grammar)