Squealing sound could be the sound of a new timing belt on an old tensioner. In my experience, the sound usually goes away after a few thousand miles after the new timing belt. I'm on my second timing belt, but the second time I had the tensioner replaced and didn't get the squealing like I did after the first. I also think my mechanic perhaps put the belt on a bit too tight.

Back to the engine racket, Mine happens just as you describe. Doesn't do it under harder acceleration (or at least I can't hear it... might just be shadowed by the sound of the engine itself) I mostly hear it when driving through parking lots or neighborhoods.. but I stopped paying any attention to it many thousands of miles ago.