Generally FC seats are taken by business travelers and they don't usually travel on Saturdays.
Tour groups on "leisure" routes would be an exception--is FRA-LINZ a "leisure" route?
Yeah, most def (not the entire route Dortmund-Vienna, but it's mostly gonna be leisure travellers post Nuremberg or so).
The ICE27 is a model ICE-T train which has a relatively small 1st class--just 1 1/2 cars out of 7. That's below average for DB's high-speed trains (e.g., the ICE 1 has a much bigger fraction of 1st class coaches).