Re: How many times a day do you run the dishwasher/wash dishes?
There are 6 in our family (but the baby doesn't eat yet). I run our dishwasher once a day and wash pots/pan/etc by hand 1-2 times a day (I cook almost every meal from scratch too so my p and p's add up!). I don't run the dishwasher unless it's full even if it means waiting till the morning (then I just run a rinse cycle before washing). I really just put in there: plates, bowls, cups, and silverware.
We don't use paper products either. If it's just sandwiches and pretzels or the like at lunch then I just set it on the table... my little ones take everything off their plates anyway before they eat!