Welcome to the forums Chris & congrats on Max.....three weeks is not a lot of time for Max to get used to you...you don't look like his parents and siblings and I'm pretty sure you don't speak the same language...when you take him into another room, you're the only thing he knows in there and you have not yet scared him or shown any aggression toward him, so he stays with you, but in a larger room, that he is familiar with, he runs because you've clipped his wings so he can't fly away from you. Unlike puppies or kittens, it takes companion birds some time to accept human flock mates, a good way to get a bird to accept you is to sit next to its cage, talking to it & occasionally feeding it treats through the cage bars.....you need to realize that you, your house & everything around Max is totally new, so you need to be patient with him...it could take a few weeks, but if you are not really patient and let him do things on his own, it could take a few months.....in the mean time, you could spend your extra time reading up on how to train Max to not bite, to not scream, even step up & step down.....
You may have read about a bird's honeymoon period, this will be it, when Max is learning how his new home operates, then when he has an understanding of it's operation, he will begin exhibiting a newly acquired attitude...actually it's always been there all along, but he's been biding his time until he's ready to exhibit his intention to vie for a higher position within the flock...even though he is himself a new flock member.....
Good luck.....