The easiest way to test is to turn off WiFi on your phone and connect to your home computer via cellular once everything's setup.
I don't use Teamviewer to remote back into my home machine but I'd recommend disabling any setting that causes the machine to sleep (to avoid sleep/wake related issues) and turn the display down to zero brightness (black) when you leave home. Battery settings won't matter much if the Mac is plugged into AC power so you should focus on your PA settings.
Wake for WiFi requires Bonjour to work via Airport devices, if you're using a Linksys router for example, that setting won't do much for you. The setting's there to allow Airport access points to wake your machine (if it was sleeping) when there's a request to access that machine.