If you run multiple awk commands, the variables used are not shared. If you want them to be shared, you could combine the commands into a single program:
awk -F ',' '
$12 ~ /<WORD>/ {count++}
'$12 ~ /<WORD>/ && $13 ~ /<DATE>/ {count2++}
END {print $count-$count2}
' file.csv
However, your three specifications seem to simplify to:
print the number of the rows of a csv file
file.csv
which contain a specific word in column 12 and which do not contain a specific date in column 13
awk -F, '$12~/word/ && $13!~/date/ {n++} END {print n+0}' file.csv
where /word/
and /date/
are regular expressions that provide the required word and date respectively.
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solved How to create a logic that substract results of two awk logics?