Can you get a ride to your next flight if it's Business class LH after arriving in First?
Not unless that J flight is taking you to MUC and you're departing in LH F from there.
(The same exception may also apply to LX F from ZRH, but not sure.)
Also any chance in the world the car picking us up from the plane when we land would take us to the FCT if we're the only ones they're picking up on our flight?
You're not entitled to a car from the plane unless you arrive and disembark from a remote stand, something that happens less than a gate position.
If you do land at a remote stand, and you're connecting to another LH F flight, they will take you.