Would a laptop with a native resolution of 3840x2160 behave the same as a 1920x1080 one if the resolution is lowered to FHD? Would getting a UHD laptop and using it in FHD be a logical thing to do if you don't intend to use the 4K capabilities but would like to have the option to?
Yes, it will be exactly the same under the same conditions (panel of similar quality, etc). Probably even a tiny bit better because space between adjacent pixels will be likely lower and therefore less visible than on a native Full HD display.
This happens with no downscaling problems because there is an integer conversion between 3840x2160 and 1920x1080 (both width and height are exactly half, so 2x2=4 píxels of a 2160p display correspond exactly to one pixel of a 1080p one). There is no need to interpolate pixels on an exact scaling, so image will not be blurrier.
No it would be lead to better performance as your GPU would have to render fewer shaders.
Your screen will look blurrier at the lower resolution as image will be upscaled from 1080p to 4k though.
I would advise buying a machine based on what you need not what you might want in the future in any case. By the time you think you need 4k, the machine you have will probably be outdated and you will have wasted a lot of time looking at blurry images
Would a laptop with a native resolution of 3840x2160 behave the same as a 1920x1080 one if the resolution is lowered to FHD?
No, it won't behave exactly the same. For full screen applications, this may actually reduce your performance (especially in poorly coded games, which will render at max resolution supported by the GPU, and then down-scale the resultant frames to the display resolution). Additionally, the image may appear a bit more pixelated (if it's running at native resolution, sub-pixel smoothing is more effective). On the other hand, the image may look brighter, because the dead space between physical pixels won't be as visible.
Would getting a UHD laptop and using it in FHD be a logical thing to do if you don't intend to use the 4K capabilities but would like to have the option to?
As a general rule, I would say no. Run the screen at it's native resolution, and then adjust the scaling instead of just dropping the resolution. You'll usually get a better looking image this way, and it will typically also use less power (because the OS is drawing things at the appropriate size, instead of relying on the GPU or display to scale them to the right size).