You can count occurences of XX in col A, for instance, with this
formula:
=COUNTIF(A1:A10,"XX")

Count occurences of AA in col A with BB in col B with this:
=SUMPRODUCT(--(A1:A10="AA"),--(B1:B10="BB"))

COUNTA() counts non-blank cells, and a cell with a space in it is
non-blank, to Excel. If you are sure that the cells contain only one
space, you could use this formula:
=COUNTA(A1:A10)-COUNTIF(A1:A10," ")
That counts your non-blanks and nets out the cells with one space.