Shouldn't Harry have expected Voldemort to rise to power soon, after he heard Trelawney's REAL prediction & Wormtail escaped??

The thing is, the resurrection potion was very complex. Remember the plan Voldemort formed? They had to be in Little Hangleton for the Bones of Tom Sr. They also needed a way to get Harry out from under Dumbledore's nose. Logically, the resurrection could not have happened any sooner.
Also, Harry actually forgot that particular prediction, as he had other things on his mind at that time.

Yes.

When he remembers the prophecy the siku after Pettigrew had escaped, he does worry about it. He warns Dumbledore. But I think that Dumbledore's reply was so carefree that Harry stopped worrying, and eventually forgot about it.