As to pure sine wave inverters, these do not truly exist. All inverters work by taking the DC voltage from the batteries or other source, and chopping it onto the output lines. This is done with solid state devices such as IGBTs. The smoothness of the output power is determined by how fast the DC level is switched. All inverters put out high frequency harmonics. The general method is to run the output of the inverter through an inductive device such as a transformer, the reactance of which tends to smooth out the switching impulses.

Many home appliances could care less about the noise on the power lines. Some home electronics are sensitive and should be run of inductively isolated circuits. Your phone system is most likely not all that susceptible, it probably has it’s own power supply that creates the local voltages. These supplies are usually switchers these days, which are just a variation on an inverter. I would talk with the phone system supplier to determine if there is a problem.

Batteries: I would place all the batteries in a central location, for safety and connivance. As to the number of batteries needed, you will need at least 15 in each bank to give you 160 VDC. This will then come down to the 120 VAC that you will want out of the inverters. The total number of batteries you will need is dependent on the peak instantaneous current demands of your systems. The current draw can be determined by I = E/P where I is the current, E is the voltage, and P is the power. You list 1/2 MegaWatt per home per month, but what usage do you expect at any given moment. The 1/2 Mega Watt per month would only come into play if you intended to run the entire system off batteries for one month, and I’m sure that you don’t want to do that. You need to determine how much power you will be supplying at a given time and size your battery array to that usage.