Should I file a separate insurance application for each grant/scholarship?
Yes. Each grant/scholarship is handled as a separate insurance instance, so each one requires a separate insurance application.
You can have several insurance policies simultaneously valid for different grants/scholarships. If the grant/scholarship provider has not specified a work period for the awarded funds, it may be a good idea, anyway, to apply for insurance for each grant/scholarship in such a way that the insurance periods run consecutively. Thus, you will be covered by a valid occupational accident insurance for a longer period of time. The validity period of the insurance has no affect on pension accrual.