Sometimes, it's best to have the toilet removed and to pour 5 gallons of water down the Drain Waste Vent/Pipe (DWV) to see how the water goes down. Yes, it's possible that the toilet itself is the cause. When it's been removed, it can be manually inspected. By pouring 5 gallons of water down the pipe at once, you'll get a 'feel' as to 1) if there's an obstruction in it, and 2) about how far down it goes (based on the amount of water that goes down there.) Also, be SURE your EXTERIOR Drain Vents aren't clogged up w/a birds nest or dirt or something. (You know, the ones you see on people's front lawns that stick up out of the ground, and have a 'cap' of sorts on it?)
As for the whistling, try Matche's suggestions. My best to ya and hope this helps.
PS: I've re-read your original post. For now, DOCUMENT every problem AND the solutions that were taken. Date them and free-hand write your 'thoughts'. This way, if the problem goes BEYOND the 1 year warranty, you have some record that the problem started BEFORE the year was over. ANd, should you end up in court, you'll give the Judge more than he-said, he-said. Document for EVERY problem; not just the plumbing one. Keeping a journal of 'things to be fixed' as well as 'things ALREADY fixed' will go a LONG way ...