Checking is user author of number of posts?

I guess count_user_posts is what you’re looking for 😉

This is how you use it:

$user_post_count = count_user_posts( $userid , $post_type );

And it returns the number of published posts the user has written in this post type.

PS. And if you want some more advanced count, get_posts_by_author_sql can come quite handy.