In the Export dialog box just click on the Options… button, a pop-up dialog will appear : you will probably want to keep the “Header” as WAV, but click on the drop-down for “Encoding” and from the drop-down you can select 24-bit (or whatever…).
Yes. The default export format is 16-bit (Microsoft) PCM WAV.
The sample rate of exported files is taken from the “Project Rate” which can be set in the bottom left corner of the main Audacity window.
Yes there is.
24 bit WAV files are not widely supported (though fairly common in high quality audio production applications). The most “standard” 24 bit format is “signed 24 bit PCM WAV”.
FLAC also supports 24 bit (if exporting as FLAC, click on the Options button to change the output from 16 to 24 bit).