Tower Controller reported confusion and miscommunication with first responders during response to an aircraft incident on the runway.

Narrative

Aircraft X; was at FBO and requested flight following to ZZZ. After some difficulty with bad read backs; the controller (a trainee working Clearance Delivery (CD)/Flight Data (FD); GC; and Local Control (LC) combined) taxied them out to Runway XXL. The Aircraft then called ready for departure; but for some other traffic the local controller had to hold them for a couple minutes. The local controller then cleared Aircraft X for takeoff on Runway XXL. Aircraft X taxied onto the Runway and lined up. Aircraft X keyed up and reported something was wrong; then immediately that there was a fire. The Aircraft occupants then egressed the Aircraft onto the Runway. The trainer who was training the trainee was sitting next to the crash phone and picked up an old crash phone that was just replaced but not removed. This mistake was immediately realized and they then picked up the new crash phone and got the Airport Rescue and Firefighting (ARFF) units rolling. The ARFF; the first unit that called; was able to quickly get to the Aircraft and put out the fire. However; ARFF requested to go to Runway XYR not XXL; and was told to proceed via Taxiway 1; 2; cross Runway XZR at 2 to the Aircraft; but instead they went via Taxiway 3 crossed Runway XZR to Taxiway 4; then onto Runway XXL to the Aircraft. ARFF corrected themselves; but didn't use their callsign. The subsequent ARFF units were having radio issues; were not properly identifying themselves; calling for each other; and not responding to tower when called while they were trying to cross the parallel Runway XZR; with traffic on final. Once the Aircraft landing on Runway XZR landed the rest of the ARFF and OPS vehicles were told to proceed to the Aircraft; but were still having issues communicating and reading back what they were supposed to. In addition; it was unclear of the status of the airport as a whole (whether or not the airport was closed; or just Runway XXL).Recommendation: Better training for emergency response. While its slow during the summer; maybe do some full response alert 2/3 kind of drills. Get ARFF and Ops more comfortable with the Runway XZR/L configuration since its used much less then Runway XYL/R. Remove old crash phone. New Letter of Agreement (LOAs) with Airport OPS and ARFF for the different emergency levels.