To achieve -1g takes a considerable pitch down rate in level flight, at 140kts, roughly around 8-9 degrees nose pitch down per second. Nothing in the video suggests the plane achieved any g loading that was much removed from 1g. The gz if it had been recorded before the roll would be around 0.995 or so and quite stable. If the plane had been built with slats, the value would be just below 1g, and the sum of gx and gz would give a vertical vector slightly below 1g. The plane is trimmed at the start to a given AOA that will achieve that g loading. If the lift vector is inclined, the flight path angle will degrade to a steeper flight path. If the stick pusher activates, the aircraft is "pushed" to a lower AOA, and will pitch to achieve that AOA, appropriate to the stab trim + elevator forces.
A barrel roll requires more than 1g to do unless you desire to end up in a vertical dive recovery, at which point more than 1g must be applied, or the flight terminates at the interface of tin and planet. A barrel roll is normally a modest positive g manoeuvre. It describes an smooth path inclined along an imaginary cylinder, which is a nice manoeuvre, it requires coordinated roll and pitch rates to make it smooth. To get the nose to come up from the initial entry requires more than 1g, otherwise it becomes a spiral dive. When inverted, the pitch rate is reduced, if the shape is desired to be smooth, and the airspeed is normally lower than entry. In a propeller aircraft, it also requires coordinated rudder as the trim condition is changing with airspeed. A tight barrel roll may be done at well above 1g, it can be done up to the g limit of the plane but normally it is a 2-3g+/- manoeuver. 1g will achieve a near vertical dive pretty quickly. The g loading changes throughout a smooth barrel roll, but is normally at least slightly positive at the top, which is the controlling condition for an appropriate g load and consequent appropriate roll rate. A constant roll rate at varying g loads requires constantly altering aileron inputs, It is a nice coordination exercise, mores with a big radial engine or large prop, or draggy biplane.
The AC derives lift from the wings and fuselage, tail and even the engine nacelles. If vertical resultants equal weight the plane will fly in level flight, if vertical resultant forces exceed mass, the aircraft will increase in height. Aircraft don't "fall" as such, unless dropped from a crane or otherwise. A helicopter that has mast bumped and removed the rotor will "fall".
The rudder is almost always effective, below transonic speeds. The rudder is not affected greatly by AOA, it becomes relatively more effective than the ailerons as AOA increases, as aileron effectiveness reduces. There is no evidence here of a rudder input so far, normally the rudder doesn't get much exercise in flight in a jet. Some jets will apply a turn coordination rudder input in some conditions, and in this case, I would assume but do not know as a fact that a yaw damper is installed in the aircraft. Most jets end up with a need to have a yaw damper, and if the wings are swept, then that becomes near certainly a necessity. A yaw damper failure can cause an initial roll like this, and may be a factor, however aileron or rudder remain available to compensate, they are normally very limited authority [UA585, US427 are cases where a failure mode of a yaw damper resulted in a large deflection of the rudder by the initial input of a yaw damper]
Speed stability will ensure the aircraft is wanting to pitch to a constant AOA, and that would be ANU. Stopping the descent when at a near vertical bank requires removing the bank first, and if that is due to a stall, then the stall must be resolved to gain control authority.