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This is not the concept of "columns" (as to my understanding). Columns are repeating structures of records (or rows) in a (DB or spread sheet or ...) table or file. E.g. Col1 has "Last Name", Col2...

Your desired output format isn't clear, but maybe something like:
awk -F'"' '
{ nf = gsub(/,/, ",") + 1
for(i = 2; i <= NF; i += 2)
nf -= gsub(/,/, ",", $i)
printf("%s\tresult:%d\n", $0, nf)...

You said you wanted to count columns, but your sample output seems to be counting commas instead of columns. To count columns, you might try:
awk -F'"' '
{ nf = gsub(/,/, ",") + 1
for(i = 2; i...