is crying necessary to move on?

No, it's not necessary but it can be helpful if it helps you to vent some emotion. Other people can achieve that in other ways. I have stunted emotional processing so for me I tend to feel less the more I'm supposed to feel. I go cold I guess. It wasn't always the way but things change as you go through more and more.

Crying doesn't indicate that you're weak. Since birth it has always been a sign that you're ALIVE.

The feeling of being alive helps you move on..

Absolutely. Get it ( the emotional poison of pain and heartache) out and get on with your life.

absolutely
crying heals

No. For some people ending a bad relationship feels like a huge weight has been lifted and is reason to celebrate, not cry.

Sometimes

I suppose it depends on the individual

No never.

Crying is pain leaving the body

For some people, the release helps.

It depends on the person.