Testing relativistic mass

Yesterday's Astronomy Cast Ep. 370: The Kaufmann–Bucherer–Neumann Experiments covered:

One of the most amazing implications of Einstein’s relativity is the fact that the inertial mass of an object depends on its velocity. That sounds like a difficult thing to test, but that’s exactly what happened through a series of experiments performed by Kaufmann, Bucherer, Neumann and others.

This was pretty good relativity history, except that if you listen, you might wonder about a couple of things.

Why were they testing relativistic mass in 1901 if Einstein did not invent it until 1905?

Where did they get those formulas involving velocity and the speed of light without relativity?

Relativistic mass for electrons was predicted by Lorentz in 1899 and confirmed by experiment in 1901-1902. Lorentz got the Nobel prize for his electron theory in 1902.

Others found rival theories that were also consistent with experiment, and it took another 5 or 10 years to distinguish Lorentz's relativity from the rival theories. That research eventually concluded that the "Lorentz-Einstein theory" matches the data. It was the first real test of special relativity.