1. Is there any Logger32 user manual on internet?

Yes.   See here.  If you download but then can’t open the help file, go back to read the instructions that you missed on that web page and do what it says!

2. I have one field in my loggbook, "Country". I am just now adding my old QSO.s manually into Logger32 logggbook. I want to register "Country" manually in my Country-field. I tried to register the country name for each OSO afterwards, but I have no success. Is it possible to use the field Primary admin or Secondary admin to register the country name and get in into my loggbook?

Right-click any QSO in your logbook, then click Setup then Grid layout:

Then select (tick) the DXCC column, and drag it to wherever you want it to be shown.  Here is my logbook column setup:

Notice the 3 options at lower right: “Show DXCC Column as Country Name” works best for me.

It’s not obvious but, on the same form, you can edit the logbook column heading/title text/labels e.g. if, like me, you don’t like ALL CAPITALS.  Simply click on the second or fourth text columns then edit the text labels as you wish.  Be succinct for narrow columns e.g. the default label “QSL_RCVD” makes the column at least 8 characters wide, whereas “QSLin” lets me narrow it to just 5.

When you have finished laying out your logbook as you wish, click Apply to see how it looks.

1. I have once by mistake deleted "operator" window on the loggbook entry window and now I have to click on the loggbook entry window icon the top menu every time I start Logger32 to get the operator window back. How do I do to save the Operator window on the Loggbook Entry Window?
   
   

Select the “OPERATOR” field in the logbook field listing as above.  I’ve renamed the column “Me” on my system since my log only contains QSOs made as ZL2iFB or ZM4G, my personal calls.

73 GL

Gary  ZL2iFB