1) Multistage rockets are used to reduce the weight of the rocket thus giving it more speed.
It's better to use the term MASS rather than WEIGHT in this case. Apart from that, you're right.
2) Newton says you can't do any experiment to tell you are inside an inertial frame of reference (constant velocity or at rest) without looking at an outside source. e.g in an aeroplane
Newton actually says you can't do any experiment to tell WHAT TYPE of inertial frame of reference you're in (constant velocity or at rest) without looking at an outside source, but you can still tell whether or not you're in an inertial frame of reference (as opposed to being in a non-inertial frame of reference).
You can tell whether or not you're in a inertial frame of reference by determining whether there is a net force acting on you. e.g. if you're in an aeroplane, you may stick a ball on the end of a string (which is a bit elastic or "springy") to the ceiling of the plane to make a sort of pendulum. If this pendulum moves forward, it means that the plane is accelerating backwards, hence you're not in an inertial frame of reference. Same applies if the ball backwards, you're accelerating forward so you're still in a non inertial frame of reference. If the ball moves up or down then the aeroplane is still accelerating in the vertical direction so you're in a non inertial frame of reference. If the ball doesn't move at all, only this is when you're in an inertial frame of reference. So you can use this sort of pendulum system to tell whether or not you're in an inertial frame of reference or not.
Another way to tell is by attaching piezoelectric crystals to the moving object to see whether it is in an inertial state of reference or not. When there is a force applied on a piezoelectric crystal, it induces a small emf (voltage) which you can measure to see if the object has a force acting on it or not. No voltage --> no force --> inertial frame of reference & vice versa applies. This is the principle used in some accelerometers.
