The information to complete the nest files are well described in the userguide. Perhaps you could have another look at it, as you get more familiar with the different parts you will understand more details.
You have to put your dimension names in the first 4 rows. In your case:
xaxis= "ni"
yaxis= "nj"
zaxis= "level"
taxis= "time"
Moreover, I think your nest files are overcomplicated, with too many dimensions (some for u, some for v,etc.). You should try to make nest files with all the variables in the same A-grid to end up with only 4 dimensions. You should ask the people who provided the oceanographic files to prepare them in a A-grid, which would simplify your setup.
Then there is the starting and ending coordinates of your nest.
For the variables, I am not sure which one you need (depending on the experiment you run), but your files seems to contain many variables. You should identify the one you need. Anyway, you will definitely need to put uvel_name (short UZ in your case) and vvel_name (short VZ).
Good luck.