Heat was my concern as well when I moved my birds to our new property a week ago. In the end I couldn't bring myself to lock them up for more than 36 hours because our temps were getting in the triple digits and I didn't want to end up losing some to heat stress. Outside they have the option to find places that are shady and dig into the ground to stay cool.
In answer to your question though, if it weren't so hot, yes, I would advise keeping them locked in for a week. It helps imprint on them where home (roost place/bedtime) is. When not locked in for a period of time, they sometimes decide to sleep out in the run and then you have the dickens of a time re-training them to the coop.
For what its worth, my girls didn't try any of that and from day one returned to the coop at night to sleep, even though they were only locked in for 36 hours, however luck may have played a big part there and if weather conditions had been different, I would have kept them confined for a full week.
Regarding food, yes, I keep it in the coop full-time. First, this keeps it from getting rained on and spoiled. Second, by having to return to the coop to food, it is reinforced as "home" and keeps them coming back in.
I keep water in the run. I don't care if it gets rained on, and that way they can't ruin the bedding by slopping water around (I have ducks too, that splash water around far more than the chickens would). Having it in the run also keeps them from filling the waterer with bedding.