Typically you want to measure everything in weight for accuracy. When I'm baking breads, my water is even measured in weight. If you have 2 people measure out a cup of flour on a scale, it would be remarkable if they scoop the exact same amount. But if you have those same 2 people scoop out a pound, it'll always be the exact same amount, no matter how many scoops it takes to get there.
That being said, starters don't need to be accurate. A difference in a couple of gravity points isn't a big deal what so ever. So the "cup to a quart" idea is measuring both in volume.
I add DME when the water is warm, not boiling. As soon as you're over 120F or so, it should dissolve pretty easily & it's much easier to bring it up to a rolling boil without dealing with a crazy boilover.
After 15-20min of a good rolling boil, crash it in the ice bath, shake to aerate & pitch your yeast. Let it ferment warm - I usually leave them on top of the fridge. Foil is better than an airlock, just make sure you use plenty - I do mine in growlers & typically use a ~4" square piece. Stirplates are good, but I just swirl mine up every time I walk past them. The swirling action should be plenty to pull O2 in for the yeast.
After a couple days the action will die down. Decant off that liquid before pitching. I let mine finish out completely & crash them in the fridge before decanting. I'll just pull it out of the fridge first thing on brew day & leave it in a warm spot. By the time the wort is cooled & ready, it'll be close enough to have shock be of no concern. If you're very careful, you won't stir up the yeast pulling it out of the fridge, so I wait to decant until right before I pitch. I don't want to remove that foil any more times than absolutely necessary. It's also a good idea to flame the lip before pitching.
BN Army // 13th Mountain Division 