Birbiri- miz-i is for 'us' alone I suppose. So what are the others,
Birbiri-nize (you) Birbiri- ler-i (they) ?
The root is birbir.
biz : birbir + (i)miz --> birbirimiz
siz : birbir + (i)niz --> birbiriniz
onlar : birbir + leri --> birbirleri
For onlar, the plural -ler is optional so you can also say
onlar : birbir + i --> birbiri
after constructing it you can add case endings: birbirimizi, birbirimize, birbirimizde, birbirimizden
Am I right in assuming that the turkish sentence does not necessarily imply only 2 people in "we" (as i believe the english sentence does)? In other words, can birbirmiz also be understood as "one another"?
Nope, that would be "Kendimizi seviyoruz."
"kendi" implies the self, which "birbiri" implies reciprocity of some sort.
Does '(Biz) sevişiyoruz' imply the same meaning or there is some difference between the two?