The HIBEX rocket was a precursor to the Sprint missile system deployed briefly back in the 1970s. The rocket was only 18 feet long but had extraordinary performance(an acceleration of 100 G's!). But I can't find any data on what the airframe used for it was since it would need metal with a very high melting point/low heat conductivity but also very lightweight. So if a team of amateurs with enough money and welding experience got together I see no reason they could build a small rocket like that and use HIBEX fuel. Though launching it might be tricky....
According to Wikipedia,
HIBEX employed a star-grain "composite modified double-base propellant", known as FDN-80, created from the mixing of ammonium perchlorate, aluminum, and double-base smokeless powder, with zirconium staples "randomly dispersed" throughout the matrix.
APCP (ammonium perchlorate composite propellant) is occasionally used in high powered amateur rocketry and isn't vastly different from the HIBEX propellant in composition. The high acceleration of HIBEX is more due to the physical grain of the propellant being arranged for maximum burn rate, combined with the ratio of engine size to payload size, than anything particular about the propellant.
Somewhat surprisingly, APCP use in amateur rocketry isn't directly government-regulated -- the hobby organizations work with chemical vendors (who are definitely government-regulated) to control sales.
Apart from time-to-speed and time-to-altitude records there's not much point in going for very high initial accelerations if you aren't trying to stop an incoming ICBM. You waste a lot of energy trying to push air out of your way.
To withstand the extreme heating, by the way, the Sprint missile used an ablative coating that would simply burn away in flight, carrying heat with it to protect the airframe beneath.
"Yes", but that would sort of be silly and it would highly depend on where you live, since it may be illegal in your country to mix your own rocket propellant. HIBEX used what is essentially a precursor to modern APCP (Ammonium Perchlorate Composite Propellant), which is widely used in amateur rocketry and commercially available. Its propellant included Ammonium Perchlorate, Aluminum, Ballistite (powdered nitroglycerine, basically) and zirconium. Both the Aluminum and the zirconium were basically fuels.
It is legal in the US to make your own rocket fuel, and none of the components of HIBEX fuel are illegal per se. However, a commercially available fuel is probably a much better choice. For the record, APCP was used in the space shuttle solid boosters.