fi fits the data using the non-linear fitting algorithm. Iterations is the number of iterations between plots. If no number it given, it defaults the last number used. If none was ever entered, it defaults to 20. After this number of iterations, the data and fit are plotted, if graphing if selected. (It is by default. See the gr command.) You are then given the option to quit iterating (q enter), continue iterating and turn on graphing (g enter), continue iterating and turn off graphing (n enter), or continue with the same graphing status.
If the fi command is executed from a command file, the fit stops after the selected number of iterations and does not prompt for user input. This is to facilitate batch processing.
There is no way in general to be sure χ2 is at an absolute minimum. It might just be at a local minimum. Starting the fit with several sets of values of initial parameters and having every fit that converges find the same set of final values and same χ2 gives some confidence. Looking at the graph at least tells us we're not too far away.
It is possible to estimate the errors in the parameters once χ2 is minimized. Rather than build this into the program for people to use with more confidence than warranted, I merely make all the information you need available. You should look at the references and figure it out. This way you will have an idea of how unreliable error estimates on the parameters can be.