Question: I will be hiking 4 days in early August between the High Sierra camps in Yosemite:

* Toulumne Meadows Lodge → Glen Aulin
* Glen Aulin → May Lake
* May Lake → Sunrise
* Sunrise → Toulumne Meadows Lodge

I do not need to carry food for breakfast and dinner because it will be provided.
I need a sleep sack but not a sleeping bag because the camp beds have blankets.

Any suggestions for the appropriate size pack?

If it helps, I tend toward the 'wear the same stuff except for socks and underwear' method of dressing each day when out and about like this.

Answer: 
I have a greater swiss mountain dog. I started by getting him used to camping with tarp in the backyard and sleeping in the van, we've also been doing a bit of winter camping in a friend's garden.

He doesn't like sleeping away from home, but then he also doesn't likes being away from me. He anyways spends his nights outdoors, so temperature/fur is no problem. (His breed is typically farmyard guard dog or livestock guard dog, so he's a barker. So rather no stealth camping. He'll growl or bark when animals move around closely - which is fine if it tells the wild boars to make a detour, but rather annoying when I wake up because some racoons came along in the tree)

Tarp + tethering from a tree works well. I haven't tried a tent. Put some thought in where to tie him to minimize the chances of getting entangled with the lines of tarp or tent.

Pad: a dog quickly recognizes that a pad is softer and warmer than the soil. If they need that, they'll use it (unless they decide it's in the category of things they're not supposed to be on). I'd put it to their use at home for a while.
My dog will scratch a pad like he does when making a cozy sleeping place with his mat or some leaves and soil outdoors. Foam pads will quickly be in shreds, I'm thinking to experiment with the cloth of an old dog mat as hull. At around 0°C, he uses a pad if available. If they don't use it, they don't need it (they may prefer to make their own camp from leaves)

Feeding: my dog needs substantially more feed when hiking the whole day, and also in cold weather (probably also because he's able to run more in cold/cool weather). I observe roughly a factor 2 between full hiking day in winter compared to hot weather in summer. (But then the mountain dogs really don't much when lazy.)

I'd do a bunch of single-night out test hikes before starting on a whole week.
I have two small dogs (each about 25 pounds), and have taken them camping with me a few times. I ended up deciding that it was not really successful, that they weren't enjoying it and that I wasn't either, but YMMV.

Try setting up the tent in the back yard and getting the dogs used to it. That way they understand what it is, and you can see what issues there might be with pads, chewing, etc.

Re tying the German shepherd up, it seems straightforward to tie him to a tree. However, that's going to get awkward if you want to keep him tied and at the same time inside the tent.

I don't think a huge amount of extra food is necessary. Dogs are much more efficient walkers than humans, and in any case, exercise doesn't really consume as many calories as people imagine. In humans, hiking is about 0.4 kcal per mile per pound of body weight. Dogs are probably half that.