I am planning to install a second OS X on an external HDD, I was wondering when I boot in external HDD will it in any ways affect my first OS X installation? Will it have the permissions to write or read from it? Or will spotlight start to index that HDD? If yes how can I isolate my first installation from being affected? (without using "third-party apps" or "file vault")
In general, when you run another installation of OS X on the same Mac, the actively running installation will see the other drive as just another drive. Nonetheless, the user accounts are very likely to differ, so probably you might not be able to access files on the non-active installation without administrative privileges. To prevent this, you might want to add the user accounts with the same names and in the same order in both installations.
This might help: In Preferences, open Users&Groups and unlock the settings. Ctrl-Click on the users and open Advanced Options. The User ID of the respective users has to be the same on both installations to avoid needing Administrative Privileges to access the files on the other installation.
If you want to prevent Spotlight from indexing the non-active installation, you can add it to the privacy list in your Spotlight preferences. To do so: Open Preferences, select Spotlight. On the Privacy-tab, you have a list called "Prevent spotlight from searching this places". You just add the hard drive with your respective non-active installation and Spotlight will leave it alone.