To our knowledge there is no single unit product that retrofits to an existing hot water tank and uses both utility and Photovoltaic generation to power a heating element directly. The closest similarity is an expensive inverter that converts DC to AC.
No, a timer simply switches power on or off on a schedule from a single supply. It is not an inverter and is normally rated for AC or low current DC. It is UNSAFE to connect DC to conventional timer switches and should not be attempted.
Yes and No. Relays are used to switch and in fact a timer switch as above makes use of a relay. DC relays are available in the market, but are extremely expensive. A DC relay rated to the same specifications as a SolarHotty may cost up to $98 or more for a single relay. This relay then only provides the capability of switching DC or AC on/off with no logic controlling the switching, no MPPT or protection mechanisms. Furthermore, such relays cannot switch both AC and DC with one relay device as this would be entirely unsafe. All relays have small delay variability when they switch and this cannot be controlled. Connecting both an AC and DC source to a single relay, even if it is a double pole relay, would be unsafe. The SolarHotty therefore makes use of multiple relays internally to do the switching, but controls the input and output of the switching tied a control mechanism driven by software that also includes safety mechanisms and an MPPT function.

The SolarHotty was designed with safety first in mind, having multiple protection mechanisms to isolate the AC from the DC, protect against improper installation, over voltage protection, over current protection, lightning strike protection, ground fault monitoring and protection.
Yes, it is compatible with U.S. type water heating cylinder. Most U.S. residential hot water tanks use 240VAC which fall right within the SolarHotty specification. The SolarHotty has been designed so as to comply with the strictest of UL requirements.
Yes, the SolarHotty can be retrofitted to installations where PV panels are already installed. The required number of PV panels simply needs to be connected directly to the SolarHotty, as long as these panels meet the input specifications. In addition, PV panels can be added panel by panel as long as the total power output does not exceed the input specifications. Therefore, panels can be acquired in a phased approach.
No, a timer simply switches power on or off on a schedule from a single supply. It is not an inverter and is normally rated for AC or low current DC. It is UNSAFE to connect DC to conventional timer switches and should not be attempted.
The installation of the SolarHotty is much simpler than conventional Grid-tie inverter installation and only requires the connection of the PV panels, utility and the heating element to the device. An electrician may be required depending on the government regulations of the installation site.
The saving will result from the use of PV generated energy and is comparable with a similarly rated grid-tie inverter. The actual energy saving will depend on the installation site and conditions and the actual monetary saving will depend on the solar yield multiplied by the price of electricity as bought from the local supply authority.

Environmental conditions and usage patterns differ widely from state to state, country to country, making a one-size-fit-all estimate inappropriate.