*Please note: This is my experience but GSD's can vary drastically depending on breeding, nerves, and training, along with many other factors.*
House/Yard Size: In my opinion, doesn't matter as long as your committed to exercising them outside of your home every single day. I actually think that sometimes people with a limited yard and house size tend to be better about exercising their dogs because they can't rely on their yard all the time
And most GSD's really just want to be with their family 24/7 anyways so a huge yard is only nice for interacting with the dog.
Amount of exercise: I would plan on long (3-5 miles) daily walks at a minimum, off leash hikes would be even better. Play is good but GSD's generally need more daily structure than just going to the park for a game of fetch. They need training and interaction at a higher level than your average dog.
I've never had kids around on a regular basis so I can't comment on the kids question, but I've heard they can be wonderful
As far as the social settings go, personally, these have never been stress-free for us with our shepherd because she is reactive to other dogs. We've always had to keep one step ahead of her to avoid a confrontation. I think you'll get mixed reviews on this question... Truly depends on the individual dogs personality and socialization. It can be done (and many GSD's are wonderful in these settings) but I do think it is more difficult than it would be with other breeds.
With everything you're going to need from a dog, I would strongly suggest going with an adult rescue. I would also look for a dog that is currently in a foster home and if possibly with some history on him or her as far as the cats and kids go. By being in a foster home you'll know a lot more about him or her than you would if they were just in a run at a shelter. In my experience, for the most part, what you see is what you get with an adult dog. Puppies can and often do go through many crazy stages and it sounds like the last thing you need is another handful!! A young adult will still have many awesome years left but will spare you the trials and tribulations that GSD pups can bring
Good luck looking for a new family member!!
Oh, and by getting an adult you'll know if they're a runner or not
Even when Sasha was healthy, running was waaaaayyy too boring for her and about a mile in she'd just stop and lay down! If I took her leash off she could run for miles and miles but there was no way she'd run on leash. Finally I just gave up...