Google Sheets Formula – Search Closest Future Date Including Current Week

Google Sheets as well as other spreadsheet application handles dates as serialized number. The large number that you refer that is displayed when a cell on AL column is blank is very likely that it is the number that represents the date on the corresponding cell on column G.

Regarding returning a blank, try something like this:

=ArrayFormula(IF(ISBLANK(A:A),,"Non blank"))

Please note that the second argument of the IF() function is left empty (,,): IFS(), IF() and other similar functions return blank when the corresponding argument is empty.

If you did not insist on array-based formula, then

sumifs(C:C, A:A, A2, B:B, "<="&B2)

entered in D2 and copied around the D column, would do the job.

I don't think that an arrayformula-based solution exists, because arrayformula runs through an array once, performing some element-wise operations. You want to compare each element with all others, which is one step further in complexity (a double for loop).

But you can use a custom function, something like =runningtotal(A2:A, B2:B, C2:C) which processes the columns and returns an array of running totals. The script implementing this function is below; add it via Tools > Script Editor. The logic is quite straightforward: as said above, it's a double for loop.

function runningTotal(names, dates, amounts) {
  var sum, totals = [], n = names.length;
  if (dates.length != n || amounts.length != n) {
    return 'Error: need three columns of equal length'; 
  }
  for (var i = 0; i < n; i++) {
    if (names[i][0]) {
      sum = 0;
      for (var j = 0; j < n; j++) {
        if (names[j][0] == names[i][0] && dates[j][0] <= dates[i][0]) {
          sum = sum + amounts[j][0];
        }
      }
    }
    else {
      sum = '';
    }
    totals.push([sum]);
  }
  return totals;
}