Calculating pulse width
Your analysis appears to be pretty close. If T1 is off, the steady-state voltage across C1 is 4.4V. When T1 turns on, the left side of C1 is pulled ot .6V, which pulls the right side and the base of T2 to -3.8V. T2 turns off and stays off until its base charges back up to roughly .6 volts. Until T2 turns on, R3 and C1 form a simple RC network charging from 4.4V to -4.4V. When the voltage across C1 hits 0V, the voltage at the base of T2 reaches .6V, and T2 turns on, turning off your output pulse again.

C1 charges through R3, giving your computed time constant of 100 uS. The voltage across the cap is changing from 4.4V to -4.4V, so we want to know how many time constants it takes to complete 4.4V of an 8.8V change. That's 50% of the transition. -ln(1-.50) = .693 time constants, or 69.3 uS.