Training a 7 month old

I adopted a 7 month old border collie/corgi mix last week. He is so sweet, listens well, is crate trained, potty trained, but as he starts to get more comfortable he is starting to become more vocal (he previously did not make much noise) which is okay but I don't want it to escalate and become an issue. How can I deal with this new behavior so that it does not get worse?

He is also starting to jump up on us at random times when he didn't before. Again, I dont want this to progress into a future issue, so do we go the route of guiding him off of us with saying down and not making a big deal of it? Do we turn away from him without saying anything? Or is there a better option for this?

Also- how long should basic commands take? I was working with him 2 days ago on giving paw. I did this by holding a hand in my closed fist and allowing him to sniff until he touched my hand with his paw. By the time we finished training for the day he wasn't getting the concept of giving paw without a treat in my hand, but today he did it multiple times without a treat ever being offered (yay!) I started working with him tonight on stay. He seemed to get it some times and other times got up too quickly. I stopped training for the night because I could sense him getting reckless and only wanting the treat so he wasn't staying as well as he was at first. I know each dog is different so they will all get things at different times, but how do I know when to stop? I also worry about giving him too many treats lol.

There have been certain things that he doesn't get a treat for during training or even now. When he successfully started pottying outside, when he comes to the door and sits to get his harness on/off before/after going outside. So I know he isn't always food motivated and I am so proud of the progress so far.