Do we get the right to access the Lufthansa First Class Lounge --not talking about the FCT-- flying in F from Frankfurt to JFK on Singapore Airlines and presenting a First Class boarding pass or will it be the Senator Lounge/Red Carpet Club?

Do they still give out PJs and full amenity kits on day time flights?

The same at JFK is there a F arrivals/connecting lounge we can use while waiting for a *Alliance US domestic connecting flight?