How to fix: "HAX is not working and emulator runs in emulation mode"

Yes it should be fixed, HAXM isn't working. How much RAM is set for use inside your AVD configuration ?

768M is a good number for it, but most importantly this number has to be lower or equal to the memory usage you have set during the installation of HAXM. You can launch its installation again to modify it.

If you are on a mac you can install haxm using homebrew via cask which is a built-in extension (as of 2015) which allows installing non-open-source and desktop apps (i.e. chrome, firefox, eclipse, etc.):

brew cask install intel-haxm 

Android Studio

If you are using Android Studio then you can achieve the same result from the menu Tools ➞ SDK Manager, and then on the SDK Tools tab, select the checkbox for Intel x86 Emulator Accelerator (HAXM installer), and click Ok.