I want to run HA app on both iOS and android devices and send scripted commands with single button press to my IPTV boxes, HDMI matrix, and Local DTV tuner centrally located with my internet router. for example, push button to connect DTV tuner box to living room TV and change channel to 33-1.
It looks like HA app can do that, but do I ONLY need to buy compatible IR hardware such as Global Cache or Broadlink device? OR, must I also set up and run a separate Home Assistant server for this to work?
You need home assistant running in order to do anything. The apps are just “interfaces”. Like a browser window (actually, on Android the app is a Chrome browser). Without having a server running home assistant, the app will do nothing.
However, you can do this very cheap/easy by e.g. using a Raspberry Pi and the Hass.io method.
Home Assistant does not run on Android at this time. You will need some other device that is on all the time. Most people use a Raspberry Pi 3 and dedicate that as their Home Assistant server.