Unemployment benefits and C4

Hello,
My position at my previous company was eliminated just before I signed with a new employer. My start date with the new company is two months after my last day with my previous employer. I would like to apply for unemployment benefits for this interim period.

I have two questions:
- If I apply for unemployment benefits, will my new employer be informed?
- Do I need to provide the C4 form to HR, or is it sufficient to share only the "vakantieattest"?

Thank you for your assistance.
TPV