The choice of slider range is a balance for what will be most useful / convenient. Using notch filters above 10 kHz is probably not very common, but when used it will probably need an exact value that would be much more easily entered by typing. The plug-in will accept typed values up to the Nyquist frequency.
I agree that “width” is more friendly, but “Q” is the correct name and has been universally used for decades. The term “width” is sometimes used for band pass/stop filters where it refers to the number of octaves and a higher number is a wider frequency band.
I think that “Frequency must be greater than 0” (or perhaps Frequency should be…") is acceptable since a frequency of zero does nothing.
I agree that “Width must be at least 0.01”
If this is included in Audacity there should perhaps be a brief mention in the manual regarding typed values greater than 10000 Hz.