having both name.site.com and site.com/name work

possible to have a proper subdomain like name.site.com and the directory site.com/name both work.

Not sure what you mean.
– Do you want to create a network i.e. go multisite and get both subdomain and subdirectory subsites in one installation? You can’t do this.
– Or, do you mean you installed WP in site.com/name and also install WP in physical subdomain name.site.com? You can do this.

switch to the “proper” method,

What do you mean by “proper” method?

all my previous posts no longer show

If you backed up database and server files before making any changes, you can revert back to your original installation so you won’t lose your SEO goodness.

I figured having something like blog.mydomain.com would be the more proper way of handling a domain.

I previously had it set to mydomain.com/blog, however whenever I try to load my posts using the blog.mydomain.com/post.php I get a “Internal Server Error” error.

I figured having something like blog.mydomain.com would be the more proper way of handling a domain.

It would be more proper to install WordPress in domain root, https://mydomain.com/

I previously had it set to mydomain.com/blog, however whenever I try to load my posts using the blog.mydomain.com/post.php

Something’s getting lost in translation or something. Do you mean you created a subdomain blog.mydomain.com and installed WordPress there? Because if your WP was installed in mydomain.com/blog, why would you even try to load posts via blog.mydomain.com/post.php?