How to connect macbook to tv wirelessly?

Question

Skype

We have:
- macbook pro with OSX EL Capitan
- regular LED TV
- webcam
Necessary:
​​- independent skype on the TV
- the ability to show the screen of the macbook and video from the macbook to the TV.
The Skype issue can be solved using some android set-top box, but it's not clear how to transfer video / screen from a macbook through such a set-top box.
The issue with broadcasting video from a macbook is solved using AppleTV, but there, it seems, you can’t set up an independent skype ...
Please tell me how to solve the situation?
I like the idea with android more, but I did not find how to broadcast the screen.
Thank you very much in advance!