1-Bit and 24-Bit Integer Variables, Please

Arduino uses standard C/C++, and thus is significantly at the mercy of the standards for those languages.
C is ... quite opposed to data types that you can't have a pointer to (preferably with hardware support), so this eliminates the possibility of 1-bit data types. (There was a brief window where some ARM chips supported pointers to single bits, but no one jumped on that enough for compiler vendors to notice.) You should be able to find assorted C++ libraries that support bit groups as objects of some sort, and would allow a syntax similar to what you suggested.

On the plus side, avr-gcc has supported 24bit integers for several releases now, and you should be able to "just use" the appropriate data types "__int24" and "__uint24", even in arduino code.