'Data stays in EU' is not true: the US CLOUD act means that American law enforcement and intelligence agencies can and do access data stored in data centers operated by American companies, whether or not they are on American soil.
To obey local laws
The USA is going "unlawful", so the risks are technical and real. Local laws do not apply
I have not looked at the US-EU agreement.
You don't need an agreement.
Tthe EU commission has tried to create schemes bypassing the issue, and twice they were dismantled by the EU supreme court.