These are solid fuel rockets (once they are ignited, they burn all the fuel), the longer range variant just has a reduced payload. The trajectory is what controls the range. What they have is Block 1, and possibly a few Block 1A (which is the reduced payload version). Range ~165-190 km.
There is no reason to think they need the US to provide targeting, there are a bunch of countries that field these systems and as I mentioned Ukraine has been using them for a year or longer.
There are a lot of those M39 rockets sitting around in Europe- they were taken out of service due to the fact that they use cluster munitions, and European countries are signatories to the Convention on Cluster Munitions. Any country that uses M142 or M270 launchers (Germany, France, Poland, Romania) have these stockpiled.
The M57 is the 300km version and has a regrained motor and there are very few of those even in existence.
Also just to note, the strike that was just carried out was on a warehouse 130km inside Russia. This is not the first time Ukraine has targeted that facility.