There are lots of aircraft that fly without wings and control surfaces.
Sure can. Balloons do it all the time. For a heavier than air aircraft, there a a couple of options.
Lifting body using a reaction system for stability and control. Here the fuselage itself creates the lifting force and the aircraft would use a flight computer to control the craft and maneuver it using a reaction control system. This can consist of thrust vectoring from the engines or separate thrusters, similar to those found on a spacecraft to control roll, pitch and yaw motion.
Another option is a pure powered lift arrangement ie a rocket belt or similar craft which can direct its lift engines to hold it aloft and to propel it forward.
No, aircraft do not need wings or stabilizers. However, they are very desirable for takeoff and landings.