Pack/dominance theory is totally outdated and regarded as nonsense by those who know their stuff
There's a great link explaining it that Karma has posted before, I'll find it and edit it in...
16 weeks - he's still a baaaby
Play biting (the kids feet/anything/everything) is all part of his puppyhood. It's perfectly normal puppy behaviour. He's testing his surroundings and exploring with his mouth, it's what they do
Don't tell him off for this but teach him what IS appropriate. If he's bitey, use big soft toys and encourage him over to play with those instead - you will probably have to play too as they're not much good at entertaining themselves at that age! How old are the children? If they are old enough, ask them to stand dead still if Alex starts biting/mouthing - if they squeal or make a fuss or move it just makes it more exciting for him (it's hard, I know!). Supervise all playtime between pup and kids - safer for both.
Can you put a babygate on the stairs to stop him going up? I have one and my dog's 18 months old. I could probably train her not to go up without one but it's so much easier to just use a gate. He also probably doesn't really understand that "get down" means you want him to come down the stairs.
Try to ignore the barking - if you just walk away he's likely to follow you out of sheer Cocker nosiness. Reward him (treats/cuddles/playtime/whatever he likes) when he's quiet and he'll soon cotton on. Pups are like little sponges for learning
Edit: great link posted many times on COL about puppy biting:
http://www.scallywagsdogs.com/Images%202010/puppy%20biting1.pdfPack theory:
http://www.apbc.org.uk/articles/why-wont-dominance-die it's quite long but worth a read.
