As for --
This is a common misconception. The government agrees: https://www.energystar.gov/index.cfm?c=dishwash.pr_handwash_dishwash
I'm an inveterate user of a dishwasher, as captured above. But I always wonder about this claim -- I'd totally buy it if it were possible to put genuinely dirty dishes in a dishwasher. But in my experience (and with a wide range of dishwashers, ranging from expensive to cheap) -- no. You've pretty much got to get at least the solid food off first, and that takes a fair amount of water ...
Though we do sometimes use the canine pre-wash cycle at our home, which is free (not in its own right, but for the prewash part), and happy to oblige.
People always say this, but it hasn't generally been my experience. Yes, most of the time I'll do a quick rinse or at least brush the crumbs off, but other times I've had extremely gnarly* stuck-on food that I didn't even try to clean off since I was in a hurry. In nearly every case, the dishes come out spotless. Maybe once in a dozen washes I'll find a plate that didn't
quite get clean, but a bit of hand-scrubbing or a second trip through the washer will finish the job easily.
The only time this wasn't the case was when I tried switching to a cheaper brand of dishwasher detergent. Night & day difference in cleaning ability, and the other stuff wasn't even the cheapest on the market. FWIW, I'm currently using the Finish tabs (previously Electrolux), bought in bulk from Sam's Club. No idea how that stacks up cost-wise against a cheaper brand + more rinsing, but it definitely saves on elbow grease!
(* and I'm a typical bachelor, so when I say gnarly, I mean
gnarly ;)