Does work depend on mass and velocity when energy is non-conservative? Can I affirm that work depends on mass and velocity when energy is non-conservative?
If $W = \Delta E$ when forces are non-conservative we have that $\Delta E \ne 0$, and $E$ depends on $m$ (mass) and $|\vec{v}|$(the modulus of the velocity), so, can we say $W$ depends on $m$ and $|\vec{v}|$ too in these cases?
 A: 
Can I affirm that work depends on mass and velocity when energy is non-conservative?

No, the work only depends on force and displacement vectors:
$$\boxed{W = \int_C \vec{F} \cdot d\vec{x}} \tag 1$$
where $C$ is a path. There is no mass or velocity in the above equation. The definition of work is related to the force and displacement, and not to what happens with an object as a result of this particular force, at least not directly. It does not care if the object weights 1 kg, 10 kg, or 100 kg. The force $\vec{F}$ in Eq. (1) can be either the resultant (net) force acting on the object in which case we talk about the total work, or a single force that acts on the object in which case we talk about work which that particular force does.
The total work done by a force depends on the displacement, and the displacement is defined via the second Newton's law
$$\sum_i \vec{F}_i = m \ddot{x}$$
where the left-hand side of the equation is a vector sum of all forces that act on the object (a cause), and the right-hand side denotes displacement (a consequence). Therefore, the displacement is affected by (i) object properties (mass, geometry etc.), (ii) current state (position, velocity), (iii) all forces $\vec{F}_i$ that act on the object etc. If you say that the work of one particular force depends on mass and velocity, then it also depends on all these other factors that affect displacement.
The work-energy theorem relates total work done on an object to change in its velocity:
$$\boxed{K_1 + W = K_2} \qquad \text{or} \qquad \boxed{\Delta K = K_2 - K_1 = W} \tag 2$$
where $W$ is the total work, while $K_1$ and $K_2$ are initial and final kinetic energy:
$$K = \frac{1}{2} m v^2$$
You could read the above equation as "kinetic energy is determined by mass and velocity", which is obvious from the equation, but this is not what the work-energy theorem says:

Total work done by the forces on an object equals change in its kinetic energy.

If the total work is positive then the kinetic energy increases and vice-versa. And this translates to change in object's velocity - if kinetic energy increases, the velocity also increases etc. It must be noted that the kinetic energy is an abstraction derived from the second Newton's law and as such works only in inertial reference frames!
There are several conditions a force must satisfy to be a conservative force. From the energy (work) perspective the necessary condition is

Work done by a conservative force can be recovered.

When you shoot a bullet up in the air, initially it has large kinetic energy and zero gravitational potential energy. As it climbs, its kinetic energy decreases while gravitational potential energy increases by the same amount (assuming there is no drag!). At the highest point, the kinetic energy is zero and gravitational potential energy equals initial kinetic energy. On the way down, the gravitational potential energy is all converted back to kinetic energy, so the bullet’s final velocity equals its initial velocity. The gravitational potential energy is an abstraction of work done by the gravitational force, and this energy recuperation is something conservative forces would do.
Another example are friction forces. The total work done by a friction force cannot be recovered, it is lost in the observed system. This does not mean the energy is destroyed, it only means it has changed its form from which it cannot be recovered, even partly, by simple means. Work done by friction forces is always negative since it always acts in the opposite direction to displacement, but non-conservative forces could also do positive work (think grenades and bombs)!

Does work depend on mass and velocity when energy is non-conservative?

To answer this question, separate the total work $W$ to work done by conservative forces $W_\text{c}$ and non-conservative forces $W_\text{nc}$
$$K_1 + \underbrace{W_\text{c} + W_\text{nc}}_{W} = K_2$$
From this it follows:
$$\boxed{W_\text{nc} = \Delta K - W_\text{c}}$$
The work done by non-conservative forces depends on change in kinetic energy which is determined by object's mass and velocity magnitude, and by work done by conservative forces.
