How to add the products through API

We added a code sample for that in our developer's documentation: www.hikashop.com/support/documentation/6...umentation.html#code

To insert a product you can use something like this (after including the hikashop helper file as mentionned in my previous link):

$price=null;
$price->price_value = 10;
$price->price_currency_id = 1;
$price->price_price_min_quantity = 0;
$product = null;
$product->product_name = 'my product';
$product->prices = array($price);
$product->categories = array(1, 2);  //where 1and 2 are the ids of two categories
$productClass = hikashop::get('class.product');
$productClass->save($product);

You can't just add days to prices...
What do you want to do ?

I suppose that you want to have a product with a "delivery" characteristic and several variants, each with a price. That's way more that a few lines of code as you need to handle 5 tables data. Not something that we can provide in a forum. I invite you to read the code in administrator/components/com_hikashop/classes/product.php to look at our code and see our code handling the save of the product information.
You need:
either to create the characteristic (with the values 4hrs, 24hrs, 5days) or not based on your needs.
Then, add that characteristic to the product with the characteristics array.
Then, get the automatically generated variants product_id based on the product_id from the product you just saved.
Also, get the characteristic linked to the each variants via the variant table in order to know which one correspond to which value of your characteristic
Finally, add the corresponding price for each variant directly in the price table.