Since you are going to be using a script anyway (for email generation), might as well use one for the rearrangement.

Here's a simplified example of form input data:

+---+------------+-------+---------------+-------+-------+-------+
|   |     A      |   B   |       C       |   D   |   E   |   F   |
+---+------------+-------+---------------+-------+-------+-------+
| 1 | Date       | Job   | Details       | cat 1 | cat 2 | cat 3 |
| 2 | 10/2/2015  | Job 1 | some details  | 2     | 3     | 1     |
| 3 | 10/10/2015 | Job 2 | other details | 0     | 2     | 3     |
+---+------------+-------+---------------+-------+-------+-------+

This will be rearranged on another sheet, called "Job List" below, by this script (which can be triggered by form submission):

function processJobs() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getActiveSheet();
  var values = sheet.getDataRange().getValues();
  var output = [];
  for (var i = 1; i < values.length; i++) {
    for (var j = 0; j < 3; j++) {
      output = output.concat(repeat(values[i], values[0][j+3], values[i][j+3]));
    }
  }
  outputSheet = ss.getSheetByName("Job List");  
  outputSheet.getRange(2, 1, output.length, output[0].length).setValues(output);
}

function repeat(row, category, quantity) {
  var arr = [];
  for (var i = 0; i < quantity; i++) {
    arr.push([row[0], category, quantity].concat(row.slice(1,3)));
  }
  return arr;
}

Explanation: the line with values[i][j+3] refers to various category counts within the row; j+3 is set so that j=0,1,2 correspond to 3,4,5 zero-based column indices (which mean the columns D,E,F above). For each count, the function repeat is called, which produces the necessary number of repetitions.

The function repeat inserts the date, category name, quantity of workers for that category (not sure why, but you wanted it), and the rest of the job description.

The whole thing is then recorded in sheet "Job List", like so:

+----+------------+----------+----------+-------+---------------+
|    |     A      |    B     |    C     |   D   |       E       |
+----+------------+----------+----------+-------+---------------+
|  1 | Date       | Category | Quantity | Job   | Details       |
|  2 | 10/2/2015  | cat 1    | 2        | Job 1 | some details  |
|  3 | 10/2/2015  | cat 1    | 2        | Job 1 | some details  |
|  4 | 10/2/2015  | cat 2    | 3        | Job 1 | some details  |
|  5 | 10/2/2015  | cat 2    | 3        | Job 1 | some details  |
|  6 | 10/2/2015  | cat 2    | 3        | Job 1 | some details  |
|  7 | 10/2/2015  | cat 3    | 1        | Job 1 | some details  |
|  8 | 10/10/2015 | cat 2    | 2        | Job 2 | other details |
|  9 | 10/10/2015 | cat 2    | 2        | Job 2 | other details |
| 10 | 10/10/2015 | cat 3    | 3        | Job 2 | other details |
| 11 | 10/10/2015 | cat 3    | 3        | Job 2 | other details |
| 12 | 10/10/2015 | cat 3    | 3        | Job 2 | other details |
+----+------------+----------+----------+-------+---------------+

Column F can be used for student names.

Cells containing the empty string "" appear empty but are not (isblank returns FALSE for them). They get sorted ahead of nonempty strings, which is not what you want. To avoid this, replace

if(isblank(B1:B), "", datevalue(B1:B))

by the simpler

iferror(datevalue(B1:B))

The command iferror returns its (optional) second argument if there is an error evaluating the first argument; otherwise it leaves the cell blank. Blank cells are sorted to the bottom.

A potential drawback of the above is that misformatted dates are simply ignored, while you may want to see and fix them. This is something you can address separately; e.g., have a column with

if(isblank(B1:B), 0, if(iserror(datevalue(B1:B), 1, 0))

and sum over it to get the total number of nonempty but invalid date cells.

Another potential issue is that you are sorting a range containing arrayformula. The sort may move the formula to another row, creating a mess. It's safer to exclude the header row from sorting. Replacing

var data = JobList.getDataRange();

by

var data = JobList.getDataRange().offset(1,0);

would do it.