Yes, it allows configuration of all the above. It's in the Settings section.
They will not interact with each other in any way, but they both would change the sound their way. Viper and software like it change, let's say, digital audio stream in Android. My software only controls the hardware chip (its filters, gain and other settings).
Personally I'm not using any of the software "sound beautificators", but if you like e.g. Viper, it's up to you. I would only suggest that you temporarily disable it, adjust sound with hardware, and then enable and adjust Viper or whatever else you use.
Never read anything like that. But I can assure you, that BD37xxx chips do not have any options to cut off stereo outputs (no HPF). If you are curious, you may search for a datasheet and refer to it. These ICs only have a LPF for subwoofer with selectable cut-off frequency at 55/85/120/160Hz, phase shift (0°/180°), and channel gain.
Addition:
You may download and install my equalizer without any HW modifications (SoundControl-1.1.apk is the latest at present), just to get an idea how it looks like and what settings it has. Then just uninstall it to bring back the stock equalizer.