I have a reseller account on a shared web host. I do NOT have root access and cannot program via a command line. Is there a way to install everything as you would a Joomla install, example: install.php?
You could try, I'm not sure how reliable it would be for a production installation. Ideally you would want to use a dedicated server or instance configured for a production or production/staging installations.
If by install.php you mean a method to install Anahita via browser, no there isn't such a thing. The reason is that you need more heavy duty tools to manage a social network and http tools aren't reliable enough for this purpose. The stakes are much lower when you are managing a CMS and you don't have to deal with as many records.
The code is on Github https://github.com/anahitasocial/anahita with the Birth releases tagged there. When you install via the composer, you get the latest Birth release. The code in the master branch is subject to change, that is why we call it an Embryo. It is the code we use to power our website and experiment with new implementations and features.