Is it possible to ride (pedal) on bike with Shimano Nexus 7 with no cable attached? Is it possible to push the bike without pedaling, when cable is unattached, or setting of shifter is not correct? I am asking, because at my last ride the setting of hub got wrong and i had no tools, so i push the bike home. (Cable was attached, but setting was completely wrong) Now i hope i didn't damaged inner mechanism. Or did I? Thank you and sorry for mistakes (not english).
Yes, that's fine.
You won't damage the hub that way, although you might damage the cable attachments if they get caught in the chain, or lose some pieces. Single cable systems work by pulling and releasing the cable, and one gear is always "cable completely slack", just as it is when there's no cable there. Like what you did.
It's just like a rear derailleur system in that regard - without the cable the spring in the derailleur pulls it to the highest gear, and it just sits happily in that gear while you ride. Your hub is similar, except that the spring is inside the hub where you can't see it.