Craft has the concepts of "singles" (pages) and "channels"[1]. You only need one copy of Craft running.
I can't recommend a file structure without knowing how your current URLs are constructed, but there definitely is a solution that doesn't involve subdomains.
Just as an example, let's say you install Craft to /craft and your existing Laravel code is in /laravel.
You'd configure your server such that "/tutorials/[whatever]" is always directed to /craft/public_html/index.php, and "/products/[whatever]" (assuming /products is your current URL prefix) is always redirected to /laravel/public/index.php.
All that said, Craft may not be the right solution for you. WordPress isn't particularly well-engineered, but it's totally free, there are millions of themes and plugins for it, and the considerations involved in deploying/managing it are discussed to death online. In short: it has a massive community, and that's important when it comes to saving time/money.
