OK. I thought window sill is as unspecific as it can be with respect to humidity and temperature (since I cannot control it; humidity in room is ~40%). As for substrate, its in the one it came (looks close to 100% peat) and water could have less minerals (boiled tap water with low mineral content). Of course I like to give it more sun, but I dont have a South facing window.
Anyway, the (new) leaves of the other plants are browning as well now, so it appears to be something more global. I will change to low mineral water and increase the humidity and see how it developes.
Thanks for all the input so far,
Bernhard