Nawiasem mówiąc in English:

Incidentally, this room doesn't have anything like an air-conditioner. All it has is a fan.

By profession he is a lawyer and incidentally a musician.

incidentally, did you see...? / ... who, incidentally, owes me £10...

Incidentally, how did you get here? (Nawiasem mówiąc, jak się tutaj dostałeś?) That isn't as easy as it sounds, incidentally. (To nie jest takie proste na jakie wygląda, nawiasem mówiąc.)

I wouldn't blame you, incidentally.

Incidentally a motorway ramp is being constructed in the neighbourhood, a few hundred metres away, of my clinic.

Incidentally, that the gills of fish are bright red is because there are many 'capillary vessels' collected there, the same as for lungs.