I do think you need to make sure he's getting enough exercise and is able to run around when he needs to.

The rule of thumb of 5 minutes per month, applies to walking on the lead, that kind of thing, where the pup has no choice other than to keep going.

It doesn't include playing in a garden and choosing to run about themselves. A border collie will get frustrated if they are in the same room all the time, with no opportunity to run about.

If the pup starts growling and staring at you, that would be time to remove him, not when he's already jumped on you and bitten you. It sounds to me like he's starting to practice his herding instinct. Staring at you, then barking and nipping if you don't move. He needs redirecting, making sure he's exercised and then given a time out if he tries it when he has no reason for it.

I wouldn't accept the nipping at all, be it hands or arms, or face personally. I'd want to play with a toy and then yelp and turn away if he nipped at me at all, especially now he's nipping at your faces.