[Lillith]

Can you simply crate him, door closed, to prevent him from going into rooms he is not supposed to? He should be perfectly fine in there for an hour and a half.

It's pretty normal for dogs to try to get closer to people, which is why he is jumping the gate to go upstairs. I understand he is a foster, so you might not want to be facilitating that type of bond. He doesn't understand your routine, so it's also normal for him to act a bit restless.

If you don't want to crate him, you can also double up on baby gates stacked one atop the other, so it's too high to the dog to jump.

 

[Lillith]

Google "Crate Games". These are games you can play with the dog to help get him used to the crate. Might be helpful in making him more adoptable, too, if he is familiar with the crate. It won't help you in the short term, but might help in the long run.

Is your downstairs where you keep the dog puppy proofed? Meaning there isn't really anything he can chew, like furniture or such? It is normal for dogs to complain a bit when they're left alone. It's good that he settles down after a while. Do you have any Kong toys? You can stuff the toys with wet dog food or moistened kibble, plug the ends with peanut butter (make sure it isn't sweetened with xylitol), and freeze it. Give the dog the Kong before you leave. The yummy treat distracts the dog, and the licking and chewing is calming. This should keep him busy for most of the time that you are out, and hopefully once he finishes he is calm so just settles in to nap until you return.