If you edit the config / config.inc.php file and add the following, you may see errors in the response (error) (1by1, which is very unpleasant when you try to understand why the creation fails). Remember to comment out the line when you are done.
ini_set('display_errors', 'on');
You also need to make sure that you add data to your POST / PUT operation using xml = <prestashop>......</prestashop> (I use C # for my Client, so this may not be necessary with PHP)
if you use ?schema=synopsis to get yours empty, make sure you look at any elements in the XML that are there as placeholders and delete them. For example, your (products) will be broken, but work if you do not.
I also added to my code that in the initial XML pass, it completely walks the tree, searches for something with the not_filterable attribute and deletes these nodes (once again there is not much documentation to find out if this thing is right to do).
EDIT: Another note in and out of language-based elements, make sure you use CDATA for the elements.
I just succeeded in creating my products by doing this, so I hope for help. I have yet to upgrade an existing one.
UPDATE: since then I upgraded to 1.5.4.1 Prestashop and started updating resources in my case
Refresh Resource
URI: http://site/api/products/1
Use Method = "PUT"
content type = "text/xml"
Be sure to remove all items that have the not_filterable attribute. (I do not understand why, but it will not work if you do not)
Delete Resource
URI: http://site/api/products/1
Use Method = "DELETE"
content type = "application/x-www-form-urlencoded"
I found that you do not need a body, so you can set ContentLength to 0. and probaly really does not need to set the content type, but it works.