How do I create a site inside another one?
It's possible, but usually not really recommended solution - as we have subdomains/multisites in Drupal.

But basicly only thing that will probably need small adjustments is .htaccess,
make sure to edit RewriteBase variable. Check out these links:

Same/Similar topics here:

How to get Drupal 7 installed in a sub-folder / sub-directory properly?

https://stackoverflow.com/questions/4122488/a-drupal-site-inside-another-drupal-subdirectory

https://www.drupal.org/node/600966

Configuring .htaccess to ignore specific subfolders: https://www.drupal.org/node/30334

https://stackoverflow.com/questions/2718406/how-to-exclude-a-folder-on-drupal-site-so-that-drupal-does-not-recognise-it-its

Also if You decide to go for multisite -> read this one: https://www.drupal.org/docs/7/multisite-drupal/multi-site-in-subdirectories

Hope this will help You :) Good luck!