Can I bring a backpack and a small duffel as carry-on on a flight?

yes you will be able to carry them on

Many airlines do allow a carry on AND a personal item. Personal item can usually be a laptop/camera bag. The typical Jansport backpack should definitely qualify as "laptop" bag (unless it's filled to the maximum and looks extremely big). I never had problems with my Jansport backpack and a regular carry on item. Watch out for airlines that nowadays charge for carry on and only allow a free "personal item". As far as weight if there are any restrictions you can try to put heavy items in your jacket and wear it. A friend of mine is a photographer and he usually brings one of these photographer vests where he can basically add most of his gear (lenses etc.) in the vest and so far he never had any problems. Enjoy your trip!

Yes. The backpack would have to go under the seat in front of you and the duffle in the overhead. However, if your flying on an ultra discount carrier or select fares on united, you may have to pay a fee for the 2nd carryon that goes in the overhead. This includes allegiant, spirit and Frontier in the US.

It depends entirely on the airline and the size of the plane. Smaller planes barely have room for one item per person, and they may make you gate check the backpack. If one item fits in the overhead and the other under the seat in front of you, you'll be fine on larger planes. Don't take someone else's overhead space.

There is no one standard carry on luggage size. Each airline comes up with their own restrictions on size, weight, and number of items allowed in the cabin.

See: http://travel-made-simple.com/carry-on-size-chart/