custom product fields not displaying in emails

That information is not loaded in the notification email. Thus you first need to load it from the database:
$productClass = hikashop::get('class.product');
$product = $productClass->get($row->product_id);
echo $product->MYFIELD;

Everything is possible but that's more complicated. You need to do yourself the MySQL query on the table hikashop_product_category with a left join on hikashop_category in order to get the category data and then display it.

You can do that directly in the template.

The code is not working ? are you sure that you have something in $row->product_id ?
Otherwise, that won't work...
By default, it should be $item->product_id not $row->product_id but I adapted the code as apparently you had $row and not $item.