How To Do Grief

My father passed away last Sunday and I was served the class of grieving the loss of a parent.
Being a scholar for almost three years, I am trying to watch myself having this experience while I completely let myself forget everything I learned.

My father fell at home while he was alone, banged his head in the wall and died. My mom found him that afternoon in a very harsh scene that shook her to her core.
When I first got the news I had no physical or emotional reaction. I had to hurry and get myself to pack, get on a flight and get to the funeral and be with my family as soon as possible, and I thought to myself at the moment that I must be doing it right because I am focused, I don’t overeat over the news, I don’t burst in tears and lose my shit, and that this is where SCS really pays off.

Then the moment I was united with my family I completely broke down. I couldn’t stop crying, sobbing, curled in a ball and crying so much I felt I am having a huge hole in my chest that will never be able to get filled.
Now I am eight days after I first got the news and looking at the past eight days I could see how much I overate and how much I cried. I both felt my feelings but also overate so much.

I found the thoughts that cause me to burst in tears each time I think them:

No one should die this way.
He was so young.
He must have suffered.
He must have lied there in pain for hours and there was no one there to help him.
It must have been horrific for my mom to see him this way.
He should have not died so soon and this way.

These thoughts create tremendous sadness for me.
Then my actions are: sobbing, and overeating.
My results are: I gain weight and feel lethargic from food, I am exhausted from crying, I process my grief.

I am not sure what to do now. Am I doing grief right?

I noticed judgmental thoughts about being such a senior scholar and how could I let myself down by overeating when I should have stuck to my protocol and just keep crying. Instead I cried AND overate.
I am unable to focus on work or exercising or anything and I don’t know if I should push myself back to work or should I allow myself to feel bad for myself and procrastinate.

I feel also grateful for having these emotions. For not being a psychopath and not feeling anything.

If there’s a healthy way to process grief, what does it look like?