Hi,
1.Let's assume in the previous operation has gone to rails Voutp-->vdd & Voutn-->0(Vinp>Vinn) then during the next transition if (Vinp< Vinn) then the circuit takes bit long time for the output to reverse, if not reset-ed using the switch. That is if the circuit is not given enough time for it to settle, then the output will have a component of previous transition too., ie, present vout=vout(1-exp(t/rc))-vout(previous)(exp(-t/rc)).
2.the output being reset-ed, ie, the differential voltage being '0'.
3. Intuitively it makes sense, since now the transition happens much faster and no need for large settling time-->looks as though the bandwidth as increased.