Flight Instructor with student reported experiencing a near miss during taxi with a back-taxiing aircraft. Flight Instructor also observed a near miss between the same aircraft and a departing aircraft.

Narrative

During a traffic pattern flight lesson with my student; an aircraft (The V35B) called up announcing they were 2 miles north of the field in-bound for the runway in use. Upon hearing this; I announced I will be holding short of the runway. The airport is currently doing back taxi operations due to a partial taxiway closure. Knowing this; I made the decision to hold short and not back-taxi to avoid the aircraft planning to land 2 miles out. I held short at [taxiway] 1 of [runway] XX.Over towards the departure end; a CL600 jet was holding short of RWY XX for an IFR departure. This aircraft was on an IFR Flight plan to head northwest of the area. The V35B landed; and pulled off onto [taxiway] 1 where I was holding short and came to a stop just a wing span length away from myself and my student. The aircraft was not clear of the runway.At this point; the V35 decided to announce a back taxi but then came to a stop after turning slightly away from us. When the V35B stopped; the CL600 announced they would be departing XX and began to line up and start their take off run.The CL600 narrowly avoided the V35B and made the decision to depart despite the V35B not being clear of the runway. The V35B also made the decision to pull of onto an occupied taxiway instead of rolling to a safer option.