It's been a while since I've had either of my 3DS consoles open but I can give you a rough idea.
All LEDs are SMD components (surface-mounted), meaning they'd have to be desoldered. SMD components are not super-easy to solder/desolder unless you know what you're doing/have the right equipment, so I wouldn't bother with these.
I'm not 100% sure about the microphone but I believe it's more or less the same thing, though I think it's also an SMD component, or at least soldered directly to the motherboard.
I believe the cartridge slot and headphone jack should be more or less identical. The old 3DS models have no IR sensor (that's what the "red LED" is, if I remember correctly) next to the cameras (that's for the super-stable 3D), so it's not interchangeable because it doesn't exist. The IR port on the back of the console is an SMD component if I remember correctly.
The charging port is soldered to the board but is the same thing. The notification LED changes places depending on the console so it's not as straight-forward to swap around.
All three cameras should be identical between all 3DS models but I'm not sure what the components on the inside look like. They probably don't have the same wiring setup, meaning they're not interchangeable.
Batteries are not interchangeable (though I'm not 100% sure about 3DS XL and New 3DS XL, but I doubt it). Battery terminals will depend on the consoles involved but generally speaking, I'd say no with the caveat that battery terminals are flexible, in more ways than one.
The circle pad itself should be interchangeable but the actual module that attaches to the motherboard isn't, if I remember correctly, as it will have a specific connection setup depending on the model. I could be wrong about that though. It's been a while since I looked at them.
The cartridge slot should be identical but given the change of position between old and New 3DS consoles, that could cause some problems. Worst case scenario, you'd need to make some minor alterations to make everything line up.
I believe the speakers change depending on the model but I'm not completely sure. Most of them should be interchangeable.
The touchscreen is not interchangeable from the original 3DS to the New 3DS as they are different sizes, but the 3DS XL to the New 3DS XL might be a different story because they're the same size. I haven't tried it so I'm not sure, but the wiring setup is different so it likely wouldn't be straightforward.
The shoulder buttons have different setups depending on the console, so they're not interchangeable.
I'm not sure what you mean by "buttons rubber domes". Most of the buttons should be interchangeable but I'm not 100% sure about that. I'd say it's probably a case-by-case basis depending on which consoles are involved.
Other than that... the charger is interchangeable, and I suppose the stylus is too (though it won't fit in the slot).
As a general rule of thumb, most all of the components have different wiring configurations, making them incompatible, especially when going from 3DS => New 3DS. If you need parts, you can usually find them cheaply on eBay or AliExpress.
