Use a CURL to work with sites without api? I have this problem.
I need to programmatically submit forms on multiple sites and receive data
The sites do not use API
This task perfectly solves the CURL.
Is there a solution to this issue Drupal way?
Maybe https://www.drupal.org/project/services?
The Services module provides API endpoints, it doesn't help to make HTTP requests.

All Drupal has natively for making HTTP requests is drupal_http_request(). Personally I'd recommend using a library like Guzzle instead, it's much more pleasing to work with, and has support for submitting forms. Plus it's in core for Drupal 8 so you know it's got the seal of approval.

PHP's DOMDocument should be more than enough to help with processing the response.