It is normal behavior, because rabbits havent been bred to not bite humans the way dogs have. If a dog bites a human and draws blood it’s unacceptable and it’s reasonable to think there’s something wrong with the dog, healthwise or mentally.
Rabbits can bite and still be normal. It’s inconvenient though, of course, so try not to “reward” the behavior. (Don’t punish him, he wont understand that).
The first bite incident you describe is as you said completely understandable. The second incident is something you dont want him to repeat. I’ve handled this type aggression by not backing off, because backing off is a reward – the rabbit bites to chase you off, if you are chased off, yay, biting works, let’s keep biting, it gets me what I want!
Your bun is young -even though he is neutered, he is in his “teens” – a natural but often annoying phase in any mammal -so it’s normal for him to be sassy, bold and try stuff.
(Of course check him over/observe him to rule out a health problem. Rabbits, like all other animals, can lash out if they’re in pain. f he is normally active, eating, eating hay, drinking, pooping etc. this is probably not a health issue.)