Can I submit a PRIMA grant if I did not change institution after my PhD, equivalent qualification to a PhD, or medical exam?

Yes you can submit a PRIMA grant without a change of institution after your relevant exam. Mobility is not part of the personal criteria which need to be fulfilled to apply for PRIMA. However, you need to plan a stay at a host institution if you did not change institution after your relevant exam and if you will not change institution for the PRIMA grant.