From the way you are describing it, it sounds to me like it is play.
My two cats do exactly what you describe you and your cat doing.
You are play chasing each other.
I linked a video of two cats playing with one another.
If you think your cat and you do something similar it should be fine.
As you can see in the video cats often switch in the middle of ...
Try to establish a play, eat, sleep routine.
It's pretty normal for cats to get hyper around mealtimes or when they're hungry, which is a likely explanation for why the incidents tend to happen when they do. Therefore, I think it would help you to change when your play sessions happen to right before mealtimes. In the wild, the natural pattern is hunt, eat, ...
It sounds like play behavior to me.
Some of the behaviors you describe are actually kitten play behavior that while uncommon in adults, a few will continue doing past kittenhood. So it may be that your cat hasn't grown out of them yet, or it may be that it is one of those cats that keeps doing it as an adult. These behaviors are:
fluffing the tail