Ok. Problem solved.
I bought a tp-link smart wi-fi plug as Ivt suggested and alternate it between two hours off and four hours on every 6 hours, just in case leaving the phone plugged into the charger 24-7 could potentially cause any damage.
Also, with regards to keeping the phone display switched on all the time, I downloaded an app that wakes the screen when I double-tap it, and since the harmony app is open when the phone auto-sleeps after 1 minute, when I unlock the phone by double-tapping the harmony app remains open. This way I could avoid the screen burn-in issue as MoodyBlues suggested and I can use the screen on full brightness and not worry about the phone overheating if I was to leave the screen on 24-7.
Thanks a lot of your help.
Couldn't have solved it without you.