Kit inspections / room inspections happen most mornings up until week 9 at least. After that it will be random as far as I know, but will depend on what your training team ask for, all are different.
Inspections in the field happen most mornings up until week 15.
Usually kit inspections in the field are done on your bivvy (rough description of your tent). All your kit is laid out and inspected, you might get around 30-45 minutes to lay it all out, but that time flies by.
The most important kit inspection to avoid is a punitive kit inspection up at the drill shed. This is punishment for certain things such as "dirty recruit", "bad performance" amongst other things.
It basically is 3 extra kit inspections per day up at the drill shed and in front of a drill corporal or Sergeant. It's something that is an individual punishment and you'll probably have bad guys from other troops there as well. It happens at Breakfast / before lunch and dinner. It isn't good and should be avoided at all costs.