I see some people coming to airplanes with lot of plastic bags, often containing something bought from airport shops. Don't these count towards carry-on baggage allowance? Could I bring more carry-on stuff from home by using plastic bags?
It depends on the airline.
Jet Blue makes no mention of airport shop items in their carry-on policy, but the United Airlines policy states that "a limited amount of duty-free merchandise or food purchased in the airport" doesn't count against the carry-on limit and the Delta policy doesn't count "food or drink purchased after clearing the security checkpoint."
Carry-on items from home would count against the carry-on limit in these situations.