I don't know why clicking the N1MM desktop icon would launch another program, but you may be able to figure that out by right clicking on the icon, then Properties, and looking in the "Shortcut" tab at "Target" -- which shows you the .exe file to which the icon is pointing, and where it's located. If you did a standard installation of N1MM (accepting the defaults in the Instalation Wizard), that location should be:
C:\Program Files\N1MM logger\N1MM Logger.exe
Once you get that squared away, the first time you run N1MM or any newly-installed update, RIGHT click on the icon, and then click on "Run As Administrator".
You need to do that the first time, (but only the first time) you run the program or any update. After that just double-click the icon as you would to run any other program.
I don't know what Error 429 might be.
Once you get N1MM running, click on the Help menu, then Manual, view a pdf of the very extensive (400+ pages) operating manual. Save the file to your computer so that you can refer to it off-line. Start reading though it. The first 50 pages or so give you the basics on how to set it up and use it.
The message you're getting about the countries list not being up to date is telling you that you need to download and install the latest available DXCC countries file (wl_cty.dat) from the Internet. You do that inside N1MM by clicking on the Tools pulldown menu, then Download Latest County File (you must have an Internet connection running) which will take you to the http://www.country-files.com/cty/
Scroll down that page to wher you see: "N1MM 8.6.2 and later" and click on the "WL_CTY.DAT" link to download the file and save it into the C:\Program Files\N1MM logger folder. Then, back in N1MM, run Tools -> Import Country List from downloaded file into the database you plan to use.
Once you get the hang of it, N1MM is a GREAT program.
Best of luck.
Mel - KS2G