Why doesn't Country show a total of 150 images. Sometimes the top level keyword shows a total count.
The counts shown in the Keyword List Panel show the number of pics to which the keyword has been directly applied and does not include the number of pics to which descendant keywords have been applied. For example, suppose you have Country > USA > California > San Francisco, and you have 5 pics to which San Francisco has been applied and 2 pics to which California has been applied. Then the Keyword Panel counts of Country and USA will be blank (0), the count of California 2, and the county of San Francisco 5.
If I select all four countries I'm expecting the count to be 100 but lightroom shows my total selection to be less in most cases.
How are you "selecting" all four countries? Depending on how you're doing it, you'll get different results.
If you're using the Library Filter bar's Text filter with the criterion "Keywords Contains Words USA Canada Mexico Italy", you'll get pics with those 4 keywords and any descendent keywords (e.g. Country > USA > California). Ditto for the smart collection criterion Keywords.
But if you're using the Library Filter bar's Metadata browser with the Keyword column, then there are two possibilities, depending on whether you have Hierarchical or Flat selected:
Hierarchical uses the same method of counting as the Keyword List panel. Flat view will show the counts of pics that have that keyword directly assigned to the pic and will not include the counts of descendant keywords. (And a little known tip: If you want to see just those pics that have been directly assigned a keyword but not a descendent keyword, use Flat view.)
Beware that the counts in the Metadata Keyword column are only for the pics actually showing in grid view. E.g. if you have a folder selected as the current source rather than All Photographs, you'll only see the counts for pics in that folder.
That principle also applies to stacking -- the counts do not include pics that are in collapsed stacks. Do Stacking > Expand All Stacks if you want to count them too.
I agree that this is all poorly documented (if at all).
I made a small mistake:
Hierarchical uses the same method of counting as the Keyword List panel.
Hierarchical mode in the Keyword column only shows counts for leaf keywords. It never shows counts for a keyword with descendants, even if that keyword is directly applied to pics.