I read your description of GSDs to my husband and he said "sounds like GSDs".
Being able to attend doggy daycare is not characteristic of the breed. If one wants a doggy daycare, dog park dog they should not get a GSD. While some may have the temperament for it, they really aren't supposed to be gregarious dogs. When I worked at a daycare, the only GSD that was able to come long term was my own and she only enjoyed it because she was able to be with me all day long. It would have made her very sad to be left there all day. We had several GSDs who would come and do nothing all day, every day but wait for their owner. And a few who seemed to do fine until they got really comfy there and started having issues with certain other dogs.
Above all else, GSDs want to be with their people and have a relationship with their people. It can almost be hard to appreciate without having been a good GSD's person. You are their entire world. I don't find good GSDs stubborn, they have a pretty strong desire to work with you. However, they can have their moments in every day life where they want what they want and when and it's hard to sway them from that. GSDs can bond very strongly to dogs they live with as well, although sometimes there is the opposite issue (more on that later). They don't tend to tolerate situations that involve being left with strangers all that well. Again it is not characteristic of them them to be gregarious. It is characteristic of them to want to be with their people, their group or in their home. Things like boarding just don't make sense to them at all I think.
I'd say the screaming in excitement, frustration or because they are upset is not uncommon at all. I had three and only one screamed (Jora) but did she ever! If she was locked away when dinner was being prepared, you'd think a dog was being killed in the house (she really loved dinner time). She also screamed when I was cutting her toenails, screamed in excitement while waiting to do agility and screamed when I worked other dogs. Of course, I have Belgians that scream too but usually over different things.
Mine were all crazy food obsessed dogs (high food drive). They would stuff themselves until they looked fat and want to eat more. They are also very clever and great problem solves. This can be a problem. The two girls (Jora and Lexi) both learned to open up cupboards and the pantry, which required some pretty tricky child proofing. Jora figured out the first two childproof latches and how to pull a large cupboard drawer out to get to the garbage. Lexi figured out how to open the fridge and the pantry (which has a regular doorknob). Jora once got into the pa pantry and ate several pounds of raw potatoes and most of a bag of cat food. I got home from work, took one look at her and thought she was bloating, so took her to the ER clinic. At the clinic, she was begging for treats from the receptionist who told me " I can see why you think she's bloating but I've never seen a bloating dog in such a happy mood begging for food". The diagnosis after an xray and several hundred dollars was "she's not bloating, she just has a lot of stuff in her stomach".
My three were from different lines - Jora was from German show lines and Lexi and Doogie were half sibling from American show lines. Jora had a near perfect GSD temperament, to me. She was super trainable, so very smart, so willing to work, so devoted, so driven and also had very serious guarding/protective instinct. The two American lines differed from her in some ways. Doogie was also extremely devoted and very trainable and very lovey/needy in the way boy herding breeds can be. He was protective to the point that it was a problem, lacked the judgement Jora had and was a bit intolerant of too much interaction with strangers. He got progressively worse, until he really wasn't trustworthy to take everywhere. Then he started seizuring and ended up dying quite young because of that. So I don't know how much of his issues were related to brain problems and how much was genetic temperament. Lexi was sort of "different" for a GSD. She had a high food drive, high prey drive but not much work ethic. She was a bit lackadaisical
Extremely good problem solver and she definitely had a bit of stubbornness to her, especially as she got older. She was the least guardy of all of mine and had no protective instincts except for a bit when strange people walked into the house without knocking (something that generally doesn't fly with GSDs) or came up to the fence. She didn't scream but she barked a lot. Recreational barker - barked because she liked to hear herself. barked and barked whenever she was outside. Also whined and carried on and "talked" about things all the time. She wore a bark collar during certain times to keep her quiet outside but eventually, she didn't really care about the correction and would bark through it, so I gave up and just tried to manage it so she wasn't barking too late or too early.
The biggest challenge I had with the GSDs was that all three were dog aggressive to some degree and DA or selectiveness or intolerance is a pretty common trait in the breed. Lexi could be a bit on leash aggressive with other dogs, which I was able to work her through. She also viewed very small dogs as prey (although she was awesome with all of my puppies and litters). Doogie was aggressive with some other males as he matured and his sire was as well. Jora was aggressive with any other female in the household. She could go tot daycare, friend's houses, trials, pet expos, etc, etc and never have any issues. But mature bitches living in the same household didn't ever work long term. It didn't matter how appropriate they were, how submissive they were or if she was raised with them. Her and Lexi lived together peacefully until they were about 3 years old (I got Lexi around a year old, had Jora as a puppy but they were almost the same age). Once the fighting started, it just got worse. They were kept totally separated and if they got together, they would start fighting immediately. That is the biggest reason I don't have another GSD. Same sex aggression is pretty common in the breed, happens in all lines and isn't something that can be easily predicted. Many people with GSDs living with same sex dogs end up in a long term crate and rotate situation.
The biggest issues that I have seen people have with GSDs are not appreciating just how guardy they can be and not training/managing them appropriately. And the dog aggression/reactivity/intolerance issues. Many can also be very bad about handling, especially from strangers (such as vets or groomers), so they need to be socialized and trained to accept such things at a young age. They can also be pretty high energy and some can be a bit destructive as youngsters. Some GSD people also refer to GSD babies as "landsharks" because they are so mouthy, grabby and bitey.
So that's my GSD experience in a nutshell. They were my first love and I may have one again some day, if my situation changes. I'd probably only have one if it could be the only girl or only boy in the household though and considering I have multiple bitches and a boy puppy, that won't be any time soon. They're great dogs for someone who wants a dog who will be totally attached and devoted to them. Who is very into their dog and enjoys doing lots of interactive stuff with their dog, socialization, early training and developing the dog into what they want and who are willing to properly train and manage a dog with this breed's tendencies (protective, guardy, potential for dog issues).