All these weapons count as non automatic weapons and thus work with either Gunslinger, Rifleman or Sniper respectively, except the Cryolator which is counted as a heavy gun and thus works with Heavy Gunner.
These weapons produce radiation damage, including both direct damage from explosions and damage over time from exposure and poisoning.
Uniques are typically either bought from merchants or are quest rewards.
Normal and legendary weapons will change their name when mods are applied, unique weapons will not. and shows the damage caused by a single click of the mouse/trigger.
If a player character puts unique and legendary weapons in a container in a settlement, nearby NPCs, like settlers or even enemy attackers, can randomly take them and they may be irretrievable.