wp_publish_post() function not work correct, because need to generate url and define author. Post added via User Frontend Pro plugin. Posting via admin panel works correct.
When WordPress gives you errors such as that the post needs an author and permalink, it is best to figure out a way to provide these. Otherwise you are asking for trouble further down the line. You might find a way to force it, but it would be an uphill battle. WordPress is like a spiderweb of connections, and you would be severing several strands.
Your question sounds like it might be better directed at the creators of User Frontend Pro, as they are the ones who will be familiar with how the posts are being created and how that result is intended to fit into a workflow.