No, not specifically. You can host them on InfinityFree because WordPress is decently universal and only requires PHP and SQL. But that’s different from a host being “optimized” for WordPress. You may have noticed that trying to host an exceptionally busy WordPress site, or using demanding plugins can easily make hosting accounts reach their daily RAM and CPU limits.
It does when the API connections come from anywhere but the WordPress installation itself. This includes anything that can publish WordPress posts remotely.
Admin has said in the past that using a workaround to do something that users aren’t intended to be able to do is frowned upon.