Mr Jeffrey needs help!🤓

Hello all this is mr Jeffrey my sweet kitty!! I got him off Craigslist ! The op wife was pregnant & they had way to many cats to take care of so I adopted my sweet cat Jeffrey in December! Come January & we now have a puppy! He is the cutest , he’s currently in this biting phase where he’ll bite mr Jeffrey s whiskers or tail or his body or bark at him & it scares him , I try to reinforce sometimes the cat swats back but I feel so bad is this normal? What do I do?

M