Goldie, the answer to your questions is the same as it would be to any question that starts, “Why do we do this on such and such a day, but not on a differnet type of day?”
Rosh Chodesh Av is a different Rosh Chodesh status from the others. Why are we not mevareich the chodesh on Tishrei – because Rosh Hashana has a status beyond merely being another chodesh. So does Av. It is a time of mourning for the Beish Hamikdash, and we therefore treat that specific R”C with a different status than another one.
When a halacha for one day is different than for another one, the answer is always, that this specific instance calls for a different halacha.
As to the laundry, you should rtry to always have enough stuff set aside so you don’t need to do laundry during this time. But if you have small children whose clothing gets dirty, it can be washed. You should ask your rov about the other things.