Do pv inverters produce ac voltage?
PV inverters create voltage and current, yes.
However, the above author is mistaken in that you cannot have current without a voltage.
You can definitely have current without voltage. A superconductor is one example of this. By definition, a superconductor cannot have a voltage gradient across any two points in it, otherwise there would be resistance to currents.
Also, if you are not working in a high-power industry, wires can be very well approximated as being able to carry currents without having a voltage across them (although this is not strictly true)
Active Power P and reactive Power Q. What are their signs are source and loads?
Power inputs (contributions if you like) to the grid simply add up arithmetically as do the the various loads in terms of the power they consume. The grid itself consumes a small percentage all the power it transmits due to the resistance of its conductors and transformer windings etc.
One of the main tasks of a grid control centre is to balance power input and consumption in order to maintain the system frequency.
How do I calculate the value of inductor and capacitor in DC-DC converter connected to DC-AC inverter?
Use the equation E = L (DI/DT). It is dependant on the frequency, the voltage and the inductance value. To insure continuous operation, the switch must turn on before the current goes to zero in each cycle.