1: The voltage detector IC output actively switches high and low, depending on the sense voltage.
Once the two transistors switch on, they "lock" each other on and will stay on down to probably something like 1.5V or so.
The voltage detector output will go high at the threshold, eg 4.2V, then go low again as soon as the voltage drops somewhat below that - so it will "fight" the collector of the PNP transistor now passing current to the base of the NPN transistor. That wastes energy in the capacitor and may damage the voltage detector.
Adding a series resistor to its output limits the current to safe levels.
A diode such as a 1N4148 would actually do the same thing but better still, preventing any reverse current in to the voltage detector output. (Anode to detector, cathode to NPN base).
2: The two transistors, once triggered, are directly shorting the capacitor in parallel to the motor and taking a large proportion of the stored energy - when the PNP one turns on, its just got the NPN base-emitter "diode" in series across the cap, with no current restrictions at all.
It's job is only to hold the NPN one on once the circuit triggers, so it can have a resistor in series with its collector to limit the current through it and the NPN base, leaving far more energy for the motor.