Can I allow only some Health data or change permissions later?

Yes. You choose which data types Calsa can read or write in the phone's system permission screen. You can change them later in Apple Health or Health Connect. Calsa's connection screen shows what has arrived and provides a route to those settings.

Turning off a type in Calsa stops its use there. It cannot grant permission that the system denied. Apple Health does not reveal a denied reading permission to Calsa, so no incoming data is not proof that access is denied. Connections are available in the mobile store apps.