Wiring – Dimmer switch gets very warm – almost hot

First of all, when you read about a "50W LED", it is certainly saying that it outputs the equivalent light of a 50W incandescent light (although that is often a exaggeration). That "50W" LED actually draws less than 10 watts. This means that it draws much less current and emits much less heat, both of which are the factors that typically limit the allowable light in a fixture.

You'd be able to replace a 50/100/150W 3-way with a lower wattage, even if staying with incandescent.

Second, unless the LED light is marked "dimmable", don't try to use it on a dimmer. You may damage the dimmer, light, or both. Even if the light is dimmable, some dimmers will not work well with a low load: a dimmer that works on a 100W light bulb may not work on an equivalent-light-output 13W LED. They make LED/CFL specific dimmers that may work better.

As for the 130V R40, that is probably a "long life" bulb. Running an incandescent at lower than rated voltage extends its life. Therefore, they make 130V bulbs to run longer on 120V. Just use LEDs rated for 120V.

As for your existing florescent lighting, I assume you're talking about the straight tube type. For a fixture that old, it's probably less efficient that newer florescent fixtures or LEDs but still much more efficient than incandescent. This is harder to replace with LEDs, just due to the area covered. There are LED tubes made to replace florescent tubes but they are still expensive and generally require re-wiring the fixture. These are most often used in commercial applications.

No, this really won't work. Suppose you have 2 dimmers at 20% and 50%. You are hoping the effect will be multiplicative, that is, 50% of 20% is 10%. It won't.

Two SCR dimmers in series will, at best, give you the lower dimming level of the two, i.e. 20%.

A PWM dimmer, commonly used on dedicated LED circuits, pulses at its own high frequency. If you have two of them, they will pulse at different frequencies. This will create a much lower "beat frequency", in music this is what makes it annoying when instruments are out of tune with each other. In light, this would look like pulsing or shimmering. You won't like it.

Actual LED emitters can be dimmed very effectively to absolutely any light level. Turn the LED on for 10 microseconds and off for 990 microseconds, you will get 1% brightness - they can be controlled that precisely. It's a lot harder in built commercial products, which have to work with a variety of existing dimmer technologies made for incandescents, and also hit a "price point" that will make you snatch it off the shelf at Home Depot. The result of these compromises is lousy dimming range.