First you should not read files like that, you could instead use a `while read` loop like:
while IFS=, read -r id name nat sex date heigh weight sport gold silver bronze; do
...
done < "$file"
Next you are using arithmetic expansion to compare what I'm assuming are strings which will not work, instead of `(( nat == "$1" ))` for example you probably want `[[ $nat == "$1" ]]`
Assuming your input file just contains only integer values in the gold, silver, and bronze columns you could use this instead:
#!/usr/bin/env bash
file=input.csv
c=0
sum=0
while IFS=, read -r id name nat sex date heigh weight sport gold silver bronze; do
if [[ $nat == "$1" && $sport == "$2" ]]; then
((c++))
((sum+=gold+silver+bronze))
fi
done < "$file"
printf 'Count: %d, Sum: %d\
' "$c" "$sum"