Roped solo free climbing refers to top roping on a fixed rope or to a traditional (aka trad) rope solo free climb.
Rope solo aiding involves fixing the rope to an anchor and connecting yourself to the free end with either knots or one of the various modern devices designed for roped soloing. Then the pitch is led as a standard aid pitch would be led.
Simul solo aid is a speed climbing technique where two climbers aid climb at the same time on opposite ends of the same rope. While climbing they alternate between free, aid, soloing, and simul climbing depending on the situation.
Roped soloing is much less dangerous than free soloing but more dangerous than climbing with a partner. One problem is that in a fall, the attachment system is loaded in a way it wasn't designed for.  Also, in case of an accident, sometimes there is no one to go for help. It can also be tedious, as the climber must ascend each section of rock twice: once to add the next belay anchor, then again after descending to remove the previous one, effectively traveling the route three times.