The guns are allowed on Intelligence IDs such as LSF, MND, KPT, and BIS. They are also allowed to be used on The Core ID and The Order ID. There may be some others, but I doubt it.
Edit: Forgot to mention. It also depends what ship they are used on. For example, a Core ID Sabre with those guns, will give you 10%, but a Manta/Guardian/Templar will give you 100% with the guns. I believe all the Military ships have 100% on the guns, and of course Manta/Neph/Bastet.
Only the six that Flash listed won't have 10% of entire powercore. It kinda makes little sense, since ANC and ANB are the worst guns to offer right now. However, if you are found with them in Omicrons and you aren't either the Core or The Order - you will have a bad time.
Of course, it doesn't have anything to do with server! The only illegal thing would be if you e.g. edited your files in order to gain additional mining bonus.
Edit: The seventh faction that can use Adapted Nomad Cannon/Blaster is the Wild, but these are unaccessible to the players, unless SRP (and tons of RP) is made. Again, it's little use, since SRP Wild ID can easily ask for normal Nomad guns.
Actually the Adapted Nomad Cannons are some of the easiest guns (to aim with) I've ever used.
It feels like their projectile is big enough so you just need to right click in the general direction of your opponent.