RE: online customer form directly to case page without login and menu
You can provide to them the “PUBLISHABLE FORM URL” that is available on the “Online Case Form” under the “External” tab. That URL is only availabe if you have ticked the box “ENABLE ONLINE” in the Online Case Form setup.
In the form the customer should fill in the field for the email address (you can label it as Contact Email Address).
I hope this helps.