This is one example where using prepared statements really saves you some trouble.

In MySQL, in order to insert a null value, you must specify it at INSERT time or leave the field out which requires additional branching:

INSERT INTO table2 (f1, f2)
  VALUES ('String Value', NULL);

However, if you want to insert a value in that field, you must now branch your code to add the single quotes:

INSERT INTO table2 (f1, f2)
  VALUES ('String Value', 'String Value');

Prepared statements automatically do that for you. They know the difference between string(0) "" and null and write your query appropriately:

$stmt = $mysqli->prepare("INSERT INTO table2 (f1, f2) VALUES (?, ?)");
$stmt->bind_param('ss', $field1, $field2);

$field1 = "String Value";
$field2 = null;

$stmt->execute();

It escapes your fields for you, makes sure that you don't forget to bind a parameter. There is no reason to stay with the mysql extension. Use mysqli and it's prepared statements instead. You'll save yourself a world of pain.

'' is an empty string, it's not a NULL value.

Other DBMS would rightfully reject your update statement in the first place (because it's invalid to assign a string to a number).

If you want to set something to null then use null not an empty string

UPDATE item 
  SET item_publication_year = null 
WHERE item_id = 5

You should also use the correct literal type for the data type. '5' is a string, it's not a number . 5 is a number. Not using the correctly typed literal might result in indexes not being used.

If the column has the NOT NULL constraint then it won't be possible; but otherwise this is fine:

INSERT INTO MyTable(MyIntColumn) VALUES(NULL);

If your variable already contains null, prepared statements will do it for you without any extra code

$query = "INSERT INTO data (notes, id, filesUploaded, lat, lng, intLat, intLng)
          VALUES (?,?,?,?,?,?)";
$data = [$notes, $id, $imageUploaded, $lat, $long, $intLat, $intLng];
$conn->prepare($query)->execute($data);

as simple as that.

Any variable that contains a PHP null will be written as MySQL null. Not to mention this query is safe from SQL injection.

If case you want to set a variable to null if it contains an empty string, here is how you can do it before running this query:

$intLat = ($intLat === '') ? null : $intLat;