how to remove the double quotes in a csv

Simplest approach:

tr -d '"' <a.csv >b.csv

Use gsub() function for global substitution

$ awk '{gsub(/\"/,"")};1' input.csv                    
1,2,3,4,9
1,2,3,6,24
1,2,6,8,28
1,2,4,6,30

To send output to new file use > shell operator:

awk '{gsub(/\"/,"")};1' input.csv > output.csv

Your splitting to array approach also can be used, although it's not necessary, but you can use it as so:

$ awk '{split($0,a,"\""); print a[2]}' input.cvs       
1,2,3,4,9
1,2,3,6,24
1,2,6,8,28
1,2,4,6,30

Note that in this particular question the general pattern is that quotes are in the beginning and end of the line, which means we can also treat that as field separator, where field 1 is null, field 2 is 1,2,3,4, and field 3 is also null. Thus, we can do:

awk -F '\"' '{print $2}' input.csv

And we can also take out substring of the whole line:

awk '{print substr($0,2,length($0)-2)}' quoted.csv

Speaking of stripping first and last characters, there's a whole post on stackoverflow about that with other tools such as sed and POSIX shell.

Another solution with sed:

sed -e 's/"//g' a.csv > b.csv