What is the ERC (European Research Council)? Find more information here:

-ERC website
-Euresearch: the Swiss guide to European research & innovation

Q: Do all the PIs of a Synergy project have to be at the same host institution?

No, there is no rule which says that all the PIs have to be from the same host institution. It is more important to show that the group of PIs is exactly the one which will lead to the expected "breakthroughs". From a practical point of view, this also needs to be reflected in the working arrangements which are part of the evaluation criteria.