AirPlay on Mac computers

So, hi you guys are doing, all good?

So I have a MacBook Pro 15" Mid 2012, i5 2.4GHz with 4GB RAM and 250GB HDD running El Capitan 10.11.3 and an Apple TV 3rd Gen running OS 7.2.1.

Some time in the past I was able to use the MacBook to Airplay to my Apple TV with no issues. In the mean time I´ve stop using that options and continue doing all updates available for both machines. Now I wanted to use the AirPlay option again and saw that options no longer is showing on the top bar.

So I started troubleshooting. Went to apple support page and followed all troubleshooting tips possible, no joy. So I went and google it. I´ve encountered several people having the same issue with several types of machines and OS X installed. Also I´ve encountered this :

Use AirPlay to display video from your Mac on an HDTV - Apple Support

So according to this my MacBook Pro Mid 2010 is not compatible with AirPlay. That could be fine if I have never used that before my self. Also I do still have the options to AirPlay from iTunes or from several other apps that has the Airplay share option.

I saw this post in this forum :

airplay display

The answer sounds like Apple way of doing things, but any one else can confirm that?

Also can any one confirm what OS X will be a good one to have on a MacBook Pro Mid 2010 where all services/functionalities are available and not restricted on any way?

Thanks in advance to all and sorry for the long post.

Chereos!!!!