The bit that sounds really suspicious is "secret apps installed", though I don't know exactly what you mean by "secret apps". But if you really have new apps installed that (a) you didn't install, (b) weren't there all along but not noticed and (c) didn't appear after a system update, and a factory reset doesn't remove them, then you may have downloaded and installed a rootkit malware (there are no viruses for Android, but there are trojans, and if you install an app containing one then some can install malware as a system app. Since a factory reset does nothing at all to /system, such malware cannot be removed by a factory reset). If you have this then unless you are rooted the fix is to reflash the phone with a new set of official software (overwriting the system with a clean version). The procedures for doing this are manufacturer specific, and I don't know LGs, but hopefully someone else will, otherwise a web search should find the tools. If the phone is carrier branded (i.e. the service provider has modified the software) you'll probably need to find the carrier-specific software.
Some of the things you mention, like redirects, don't require actual malware (although malware could do it): some ad scripts will do that, and can usually be fixed just by clearing browser caches. Calls cutting out can happen for a number of non-suspicious reasons, and backlight changes don't necessarily mean anything at all. So it's really the "extra apps" that is the most suspicious.
Do note that it's unlikely that anyone has actually hacked your phone. The two most likely methods of infection are you downloading an infected app (unlikely if you download only from the Play Store or Amazon, quite likely if you install stuff from sites that offer pirated apps or sites where anyone can upload apps) or someone hacking your Google account (which would then give them access to your phone). So as well as being careful where you download from, and if necessary reflashing the device, it would be worth not only changing your Google password (from a computer rather than the phone, if you think the phone may be compromised) but adding 2-factor authentication if you are not already using it. That latter makes it much harder for someone to gain unauthorised access to your account.
