1. This model is sometimes designated as having a 66 MHz processor,

since the clock input runs at 66 MHz. However, the processor itself

is not "clock doubled", so technically it is only a 33 MHz processor.

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How does the processor not run at 66mhz if it's clock signal is 66mhz? When the first 486DX2's came out, it was truly a clock doubled processor, so how does the 68040 compare? Is my upgrade board a true 66mhz chip, (2x as fast as the LC580) or not?

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That description is backwards. The chip is really being driven at 33MHz. The '040 has two clock inputs - PCLK and BCLK. In your case, BCLK is at 33MHz and is used for all the bus signal timing, while PCLK is at 66MHz and is used for internal logic timing.

Basically, it's a 33MHz chip. Your LC 580 is doing the exact same thing, just without an FPU.