The folder is probably named /home/nodebb/nodebb not /path/to/nodebb so try. cd /home/nodebb/nodebb to go to the installation directory. If that gives the same error you can list the contents of the /home/nodebb directory by the ls command and find out the real name of the nodebb installation directory.
I've read all the docs and searched the forums several times over, but it's still not clear to me if you can upgrade across branches in one step.
For example, if I'm on 1.10.2, can I upgrade directly to 1.12.2?
In the past, I've always applied each interim release to get from point a to point b (i.e. in this case 1.10.2 -> 1.11.0 -> 1.11.1 -> 1.12.0 -> 1.12.1 -> 1.12.2).
If it's generally agreed that doing it one fell swoop is "no problem" (TM), it would save me some typing and time.
Yes it should be no problem. It used to be that this wasn't possible but now it should just work.