Yes!
Not so much with my current dog, but my last one; I had to be always vigilent. But it is good advice for all dogs, animals-and even excitable humans sometimes. It is always easier to control before it esculates or even might avoid behavior entirely. So yes; catch it before.
Oh, I am sure he does not think his bite is anything more than a play puppy bite. He does not know better. So best to not let him get excitable to biting point. He'll learn.
Yes, everyone has to be in on training. Use same words. If there is question for a good word; maybe even have family vote on good word! Makes kids aware of importance and gets them engaged.
Sometimes I use odd words cause for some reason those catch her ear best. Example, she has bad whining habit. I tried all common words. Then, one time my sister on phone said she sounds like she is squeaking, "oh, stop squeaking!" on speaker phone. She stopped! And now I say stop squeaking and it stops. Crazy. Works. She is also learning to control herself again. It all builds.
I use wait as word for "stop there in that spot" like going out doors. So I used freeze if she is running like a maniac and I want her to stop. I use stop for her to stop in her tracks like if she is walking ahead of me. Like I would use forward, left, right. More a directional term. You can use any words. But if you use stop as going through a door for running like a maniac; dog might not see that as same. One is stop from going through door and one is stop and no barrier/door? In middle of yard? My human is nuts? For me wait is like wait in bedroom while I go to kitchen. Not as strict as stay where shhe should hold same position and not shift about. But this is just me. And it works with her. And being service dog she needs subtle differences. You may not. But they are smart enough. Mine is only just 2 so "we" still are learning and just getting good attention span.
But get some reading on the "positive dog" training. A lot is catching them in a behavior. "They" say it sticks better and does not stress them. I don't know. It works. Sometimes they catch on right away, sometimes not-if so we have probably not been so clear in explaning to dog what we want. Look to ourselves first. Make sure no mixed messages. I am no expert; just learning through reading, hearing, seeing, trying.
If dog does command in one location or situation and not another, it means they have not really learned that. Maybe they learned cues from a location moreso. That is a dog learning curve and also making sure they are learning the behavior to the cue or word; not just the situation. OR it could be they are otherwise distracted.
I was told if you say it twice, and it is something you KNOW dog knows; probably dog is not paying attention to you for some reason. Mine sometimes is distracted. I tap her on her shoulder, she looks at me, and say it. Almost all the time she does it then. I also use "watch" or "listen with your listening ears" (just listen would work)
But yes; be vigilent and catch oops before it happens.
As far as other dogs, I am not best to ask as I only have one dog at a time. First dog (all mine as an adult, I grew up with dogs) was mostly good with dogs; once in a while; if I was not vigilent some dog would set him off barking for no reason I could tell. Why some dogs and not others? I never learned why. On this one, she is accepting of other dogs; if one barks at her she might get a little timid-i pat her, no big deal- and do not act like it is. And she is big girl, tall, so not many dogs taller in her experience. So if a great Dane appears, she is a little timid. I do same thing. But she is only 2. Basically I am trying to teach her that her world is not rocked by these dogs. She has gotten better. But I just do not have much experience with that. Most dogs or any animals she immediately wants to play. Why don't cats and oppossums play the right way? They act all funny and don't bow down! So this is just experience thing for her.
So, I think you do need to see a dog trainer about that. They are used to handling lots of dogs in dog groups. Maybe it is just getting around more dogs; maybe it requires more behavior modification. Also they need to really find the causes. Maybe it is being viligent? Is it protective? Or what? On mine, I cannot encourage any "aggressive" protective behavior. But she will position her lying down body between me and a stranger. With her size, no one is going to need more than that if they are up to no good. I know my dog came to a shelter, was kept in a kennel with some basic work in the "cage" with a very dominent male dog. If she gets near that dog, she gets timid. I think he puts all the dogs there in their place. I can tell it stresses her; so I just stopped going where that "bully" is. Something went on there. On other hand-flirts shamelessly with human men. And men love her. I have to watch this as she works. Be vigilent. It is harmless except that it distracts her attention from me. And that is not good if she is working. Anyway, I think you need someone who knows to watch her, or see videos, of him displaying these behaviors to make the assessment. My only comment is that maybe he does not know "you" and his new life and routines enough to "know" that he is safe and his needs are now taken care of. It might not be time yet to expect him to be "relaxed" yet. Maybe he is still holding a degree of stress? This sets it off? Just hard to say, you need person who knows to observe and comment. It is hard to say, is it a temperment thing? Can you tone it down? Is it a none of us are perfect and that is his and your cross to bear? Is he just getting over excited and does not know how to handle the situation? So he takes matters into his own paws?
All I can say, some things that I thought I would never improve in my other dog eventually did improve. It was more and constant work. Vigilence. So I guess nothing is impossible.
Sorry I have no ideas as far as other dogs. But I would have it evaluated before putting him or another dog in an undesirable siruation where somebody might get hurt. Learn what you and he need to do to respond correctly. It is probably more than just needing to get around other dogs. He HAS been around other dogs. So lack of exposure would not fit this so well.
I do continually take mine out and point out bew things. I have to. With this dog and previous, call me nuts; if there was some new to them object, like a pipe in ground, I would point and say, "pipe". Then that was it, they would move along. So let's say next is a big dirt ditch. I might say "ditch like a pipe". Silly as it sounds many many times, as soon as they heard me "name" it and act like no big a deal; it was not a big deal!
I think it sounds like you are doing right. maybe children need to be calmer in his presence. At least for now. And everyone same words of direction, everyone good boy and that is it when good is done. Maybe he needs more time to adjust. If he has a quiet spot he can go and he knows it thar is good. If he navigates in car that is good. Oh, and forgot as far as kids. Maybe being a shepherd he is seeing them as unruly sheep. You know, I have seen trained sheep dogs nip at a wayward sheep top get it to move along. So- this could be a factor too! You can decide that.
All I know, mine is VERY smart for better or worse. My other dog, a mix of other things, was smart; but this one is really smart. She shows initiative! And this is just the reason I have to show her and teach her how to behave in situations. I had to show her to settle and down in a doctor reception room and in the exam room. After learning it in mainly one office; I had to re-show her in a new doctor's office. On and on. After about 3 offices; and after I walk her around to see a new office (take in potted plants, doors, etc) she now settles right in. Then, as of recent; now knowing good behaviors; she can sometimes select right behavior on her own now! But it takes me seeing each situation as new to her; and teaching her how to do.
A story. An insurance woman stopped by house. She gave me a rolled up throw. Well dog saw it and was watching it whole visit. I could tell she wanted it a lot more than I did. So after woman left; I gave it to her. She helped untie the bow, helped unroll it, and then picked it up and placed it on the end of the bed next to her pillows! All on her own! (yeah, the only dog I have ever shared my bed with, and only because she stays in her place on top of another throw and I keep her very clean! She has her own very nice bed she uses also.) she loves that throw! She knew not to just take the throw. She knew if I gave it to her it was hers. And she thought and then figured out the proper place to put it. This comes partly as we have been slowly working on her bringing toys back inside after she takes them out and is ready to come in. So it all comes in time, and we more to learn

I love learning more about her as she learns. And I love as time goes on we understand