I have also been told these laws do not hold unless I am an inertial observer or in an inertial frame of reference

The information you provided is correct but slightly misleading. Newton's laws of motion don't go out the window in a non-inertial reference frame - they just need be adjusted a little bit to fit the frame of reference.

An inertial observer is defined to be an observer stationary with respect to an inertial reference frame. The definition of an inertial reference frame is a bit circular, and you've correctly provided it. It is just a frame in which an object with constant velocity will stay with that velocity unless acted upon by a force. So if an observer is in an inertial frame of reference and not moving within it, he is an inertial observer.

There are many ways to think about internal and external forces. I like to think of it in terms of mechanical energy (kinetic + potential) conservation - if after being acted upon by a force the mechanical energy of a system is conserved, then the force is internal. If not, the force is external.

For example, when gravity acts on a falling projectile, it converts the gravitational potential energy of a projectile to kinetic. The force of gravity does not change the overall mechanical energy of the projectile, so it is an internal force. However, the force of friction in the air takes energy out of the system, such that the projectile's velocity does not increase past its terminal velocity. As such, friction is an external force.

I have also been told these laws do not hold unless I am an inertial observer or in an inertial frame of reference

The information you provided is correct but slightly misleading. Newton's laws of motion don't go out the window in a non-inertial reference frame - they just need be adjusted a little bit to fit the frame of reference.

An inertial observer is defined to be an observer stationary with respect to an inertial reference frame. The definition of an inertial reference frame is a bit circular, and you've correctly provided it. It is just a frame in which an object with constant velocity will stay with that velocity unless acted upon by a force. So if an observer is in an inertial frame of reference and not moving within it, he is an inertial observer.

There are many ways to think about internal and external forces. The way I learnt it in an introductory class was to thinkk of it in terms of mechanical energy (kinetic + potential) conservation - if after being acted upon by a force the mechanical energy of a system is conserved, then the force is internal. If not, the force is external.

For example, when gravity acts on a falling projectile, it converts the gravitational potential energy of a projectile to kinetic. The force of gravity does not change the overall mechanical energy of the projectile, so it is an internal force. However, the force of friction in the air takes energy out of the system, such that the projectile's velocity does not increase past its terminal velocity. As such, friction is an external force.