You're welcome. Yeah there is a lot to explore in this area. the Bachalpsee was recently suggested to me by a co-worker but I was never there myself yet. Those pictures will turn out great i hope.
I'm not so sure about the camping. In general it is not allowed to camp in the wild. There are a lot of campings around lakes, but i've never heard of any in the mountains. There will most certanly be nobody to watch out for wild campers so you should be fine if you are maybe a little hidden. The police is in general very kind to tourists so even if you encounter some (which I doubt) you should be fine. :-)

Of course. Let's stay connected and if you need to know something then just ask. Maybe i can give you an answer. Right now there is a great streetfestival called Buskers in Bern. That one would be worth visiting if you are close.
Cheers and enjoy the mountains!