'from part to part' is correct or not?

Electrical engineer here.

It's grammatically correct, but it doesn't mean what you said you want to say.

When we say "part to part" in the context of electronics, we usually mean the variation between different parts of the same type. For example if you were building several samples of an audio amplifier design and some of the 2N4041 transistors you bought to use at a particular location in the circuit were noisy and others were "quiet", then you would say the noise varies "from part to part".

You could also talk about the noise varying "part to part" if you were considering different transistor types to use at a particular location in your circuit.

If you want to say the noise varies at different locations within a single example of a circuit, you can say "the noise varies from node to node" or "the noise varies from point to point".

Besides, using extensively instead of widely has the same meaning in above sentence?

No, extensively doesn't fit here. Extensively has a meaning of "covering a large area", which doesn't really apply to noise, and is opposite of what you're trying to say.

You can say the noise varies dramatically or the noise varies by a certain amount (like "the noise varies by 20 dB"), but widely is just fine too.