Yes.
While doing a workout Session, click on the timer in the top left to open the timer options popup. You can then pause it, disable it, or change the default rest time length.
You can also override the default rest time for each exercise individually! For this, open the Set parameters popup, enable the Rest time option and choose how long you want the rest to be after performing sets of that exercise.
No, it is not. The general timer is there as information for you, and the optional rest timer is there to remind you to get back to working out. The time taken between checking off sets is not taken into account either.
The only timer that is taken into account for level calculation is the one you launch for a static exercise (just like the number of repetitions).
The time taken to go through a workout does not have a strong enough correlation with how proficient you are at the exercises to be taken into account to calculate your level.