Google-sheets – Ways to iterate and append a date calculation a set number of times in Google Sheets

You don't do this by increasing the formula by a cell for each row. This is not possible.

Instead, you use as the formula

cell B1 = A1
cell B2 = SUM(B1, A2)
cell B3 = SUM(B2, A3) 

Now you can drag down the formula from B2 and B3 (don't include B1 in the selection!) for as many rows as you like.

I suppose the error message refers to the Maps service. Then converting to array formula won't help since you will still be calling Maps as many times. Here are some things you can do:

Don't call the Maps service unnecessarily. Right now, you are calling it a dozen times with empty destination and origin. Check that those are nonempty strings beforehand.

Switch from a custom function to a function that's triggered by form submission. That is, instead of putting =DrivingSeconds(...) in the spreadsheet, add a trigger that will call it on form submission. Here is how this function can look like

function DrivingSeconds() {
  var sheet = SpreadsheetApp.getActiveSheet();
  var input = sheet.getRange("A2:A").getValues();
  var output = sheet.getRange("B2:B").getValues();
  for (var i = 1; i < output.length; i++) {
    if (!output[i][0] && input[i-1][0] && input[i][0]) {
      output[i][0] = Maps.newDirectionFinder()
      .setOrigin(input[i-1][0])
      .setDestination(input[i][0])
      .getDirections()
      .routes[0].legs[0].duration.value;
    }
  }
  sheet.getRange("B2:B").setValues(output);
}

Notice that Maps API is invoked only if we have both origin and destination but do not have duration yet. Output:

+---+-------------------------------------------------+-----+
|   |                        A                        |  B  |
+---+-------------------------------------------------+-----+
| 1 | Address                                         | ETA |
| 2 | 5020 IMPERIAL AVENUE, SAN DIEGO, CA,92113       |     |
| 3 | 4699 EL CAJON BLVD, SAN DIEGO, CA,92115         | 604 |
| 4 | 8620 LA MESA BLVD, LA MESA, CA,91942            | 674 |
| 5 | 2820 VIA ORANGE WAY #Q, SPRING VALLEY, CA,91978 | 638 |
+---+-------------------------------------------------+-----+