Is a multi-sector connection included in the floor slab?

Sure, it's embedded.... But in most cases, there's still an extra cost for it.

If the material is provided by the client on site instead of being obtained through the [GU]: Would that have disadvantages in terms of warranty for tightness, etc.?

You also have to clarify this additionally with your [Versorgungswerk]. With us, they only approved a specific one, which could only be obtained through [die]. (Internet would have been possible, but the local building material suppliers did not have this manufacturer in their program).