Does one have a formula ready which says the email field must be filled and be in the correct format? thx for help

Try this:

AND(
ISBLANK(EmailField__c),
NOT(REGEX(EmailField__c,'([a-zA-Z0-9_\\-\\.]+)@((\\[a-z]{1,3}\\.[a-z]{1,3}\\.[a-z]{1,3}\\.)|(([a-zA-Z0-9\\-]+\\.)+))([a-zA-Z]{2,4}|[0-9]{1,3})'))
)