Is sengen/senga an irregular conjugation of "the bed", or is something else going on that I don't understand?
It's not irregular. It's "senga" if you're choosing to use the feminine form (ei seng), and it's "sengen" if you're choosing to to always use the masculine form (en seng).
Ahh, got it! Thanks :)
Det er godt å vite.
Here, is the gender of the adjective based on the girl?
No, trygg is both male ans female. It would only change in the neuter form where it would be trygt.
I more meant the gender is in reference to that instead of the bed. So if it was say 'bordet' would it remain as 'trygg' or would it then become neuter?