Using Newton's Laws as a starting point, they are a consequence. Actually, Newton spoke in terms of momentum. Newton's 2nd Law actually says that force is equal to the change in momentum over time (which reduces to $F=ma$ if mass is constant). Newton's 3rd Law basically gives us conservation of momentum. If two objects impart equal and opposite forces on one another, for the same amount of time, then their change in momentum will also be equal and opposite.
Energy also traces back to Newton's Laws. A combination of the definition of work ($W = F \cdot \Delta x$), the Work-Energy theorem ($W _{net} = \Delta KE$), total energy ($E = KE + PE$), and ($F = -\Delta PE/\Delta x$) will show the conservation of energy. Alternatively, if you accelerate a mass with gravity and compare the kinetic and gravitational potential energy, or a spring-mass system and compare the kinetic and elastic potential energy, you will see that they are indeed conserved.
On the other hand, the 1st Law of Thermodynamics gives us the conservation of energy independent of Newton. Furthermore, both energy and momentum are conserved in quantum mechanics, where $F=ma$ is meaningless. With that in mind, we might say that Newton's Laws (stated as regarding forces) may be a consequence of our conservation laws, not the other way around.
1)Definition: An inertial frame of reference is a frame of reference where Newton's first law applies (uniform motion if without external force).
Now if we have other frame of references that are moving relative to this inertial frame with
uniform relative velocities, then all the others are also called inertial frame of references.
2)Transformation between inertial reference frames:In Newtonian mechanics, the laws of physics are invariant under Galilean transformation. While in special relativity, the laws of physics are invariant under Lorentz transformation. The latter reduces to the former in classical limit.
Best Answer
Regarding total momentum conservation, the point is that in non-inertial reference frames inertial forces are present acting on every physical object. Momentum conservation is valid in the absence of external forces.
However, if these forces are directed along a fixed axis, say $e_x$, or are always linear combinations of a pair of orthogonal unit vectors, say $e_x,e_y$, (think of a frame of axes rotating with respect to an inertial frame around the fixed axis $e_z$ with a constant angular velocity), conservation of momentum still holds in the orthogonal direction, respectively. So, for instance, in a non-inertial rotating frame about $e_z$, conservation of momentum still holds referring to the $z$ component.
Mechanical energy conservation is a more delicate issue. A general statement is that, for a system of points interacting by means of internal conservative forces, a notion of conserved total mechanical energy can be given even in non-inertial reference frames provided a technical condition I go to illustrate is satisfied.
Let us indicate by $I$ an inertial reference frame and by $I'$ the used non-inertial frame. Assume that our physical system is made of a number of points interacting by means of conservative true forces depending on the differences of position vectors of the points, so that a potential energy is defined and it does not depend on the reference frame.
If the origin of $I'$ has constant acceleration with respect to $I$ and the same happens for the angular velocity $\omega$ of $I'$ referred to $I$ (it is constant in magnitude and direction), then only three types of inertial forces take place in $I'$ and all them are conservative but one which does not produce work (Coriolis' force). In this case, the sum of the kinetic energy in $I'$, the potential energy of the true forces acting among the points and the potential energy of the inertial forces appearing in $I'$ turns out to be conserved in time along the evolution of the physical system.