Glad you posted the question[s]. I'll do a quick explanation and description of the inverter and components.
First off, the Transistors [the components with an arrow in a circle] are used to create an AC from the DC supply [from the Battery]. The AC will be very sharp, so it will be "Square Wave". The Base [the circuit part which extends from the "Bottom" of the Transistors] is connected to some type of "Clock" circuit, which gives the "Frequency Pulses" that the Transistors use to "Turn On And Off".
This is the basic operation of the inverter. This is also very similar to an Audio Amplifier, such that the base is connected to an AC source, which produces an amplified AC signal.
The Transistors in the schematics are either PNP [The Blue colored ones], or NPN.
The PNP ones allow Positive Direction current flow to be controlled by a Negative Biased [in the Negative direction] base circuit. A high level on the base will allow a high level to flow through the Transistor.
The NPN works the same, except the charge flows are the opposite [and the base is Positive].
It would take too much time and typing here to explain the operations of transistors, so to better understand them it would be best to read a few basics manuals.
Simply, a Transistor will block current flow until some charges are drained [PNP], or added [NPN] to the base. That's the way they do an Amplification effect - very little current [and power] controls a very large current [or power].
Anyhow, the Square wave AC produced by the Transistors is applied to the Transformer, which produces a similar Square Wave AC output. The Voltage on the output is dependent on the winding ratio [common transformer]. Also, the required KVA is reflected to the supply, so what ever the load KVA on the output is, the inverter must deliver the same KVA to the primary of the transformer.
As with all Transformers, this one will reflect Impedance to the power source.
For this [or these] to work as an UPS [Uninterruptable Power Supply], the input AC is simply Rectified to DC, then connected in Parallel with the Battery [in reality, through a transfer type switch], and the output AC is completely independednt of the input AC.
AC Input / Output and even Hz can be anything desired. Frequency Inverters work in the same matter as this, except the output Hz is different than the Input Hz.
As you can see, using a very low DC voltage would require very large Transistors, plus Battery Amp-Hours would be high. The output KVA will equal the KVA in the inverter.
Although there's no KVA on the DC side, there will be an equal level of current for the entire Apparent Power on the AC side. All this flows through the Transistors.
The components that look like a series of forward and back slashes [/\/\/\/\] with the label "R" are Resistors. The components that resemble a "Normally Open" contact - with the bottom line part being curved somewhat, are Capacitors. They are labeled "C".
The Transformers are "Center Tapped Secondary" type, connected in reverse. That's how the "Home Made" ones are created! Actual Manufactured Inverters would use Transformers wound with a Center Tapped Primary and a core that works well with a high level of DC biasing current [coupled DC currents].
I have a Transformer design book which explains the techniques for making one of these spec transformers [among other spec transformers, inductors and such].
Let me know if this explains the schematics enough.