A^_B^_C
AA^_BB^_CC

wc -L file

awk '
{
for(i=1;i<=NF;i++)
    if (length($i) == good) { continue }
    else {
        print "Row "NR" contained data more than " good" in a single field"
        next
    }
    print "Row "NR " is valid"
}' FS='\^_' good="1" csv
Row 1 is valid
Row 2 contained data more than 1 in a single field

awk -F'\^_' -v OFS=':' '
{
    for (i=1;i<=NF;i++) {
        if (length($i) > max) {
            max = length($i)
            lineNr = NR
            line   = $0
            fldNr  =  i
            fld    = $i
        }
    }
}
END {
    print lineNr, line
    print fldNr, fld
}
' file

1^_1^_1

awk -F'\^_' '

  NR==FNR {split($0,clen,FS); next} # store the lengths

  {
    split($0,a,FS); # put the current line in an array
    for( i in a )
    { if( length(a[i]) > clen[i] ) print "["FNR","i"] = "a[i] }
  }
' clengths data

[2,1] = AA
 [2,2] = BB
 [2,3] = CC