If you put the pump bits back into the fridge you don't even need the hot soapy water (and you don't even need to rinse them, except for the daily big clean).

BF 3 month olds are all over the shop - some will have a time when they will feed 5 or 6 times in a couple of hours and then have a 5 or 6 hour break
Others are 2-3 hourly feeders like clockwork
Some are a combination of both of these, and many change what they do every day.

A full term+3 month baby will drink something like between 800 ml and a bit over a litre a day - which is a lot more than a corrected-age-newborn. But when Jett gets to actually be sucking, he can help increase your supply too.