Three phase four wire system is found to be most economical (conductor size and number of conductors) and efficient among all the available options. Hence 3 phase power system is used widely.
The only ways this can be done is via a motor generator or a solid state inverter. These can convert single phase power to 3 phase power, however they are generally too large and expensive for home use and motor generators are extremely noisy.In a commercial or industrial location 3 phase power is usually directly available from the power company.
A 3-phase meter measures the sum of the power in the three phases, so if power is drawn on one phase only it will still be correctly measured.
There are several advantages of 3-phase power over single phase power. First, with 3-phase power, more power can be transferred with the same amount of wire (meaning the amount of copper used in all of the conductors transferring that power) as with single or 2-phase power. Also, power is transferred more "evenly" with 3-phase power because the "next peak" is closer than it is with single and 2-phase power. The 3-phase motors run more smoothly than those run on fewer phases. Also, there are motor design considerations (one being control of the direction of rotation) regarding the motor that make 3-phase power more attractive. Use the link to the Wikipedia article on 3-phase power and skim it. It isn't long and it is quite readable.
The Scott T Connection is what you are considering. There is an article in wikipedia.org, but they say there that this concept is of historic importance only.
3 Phase power is supplied by a 3 pole supply like a breaker. So essentially yes.
how to connect power capacitor with 3 phase motor
It is in some places, but not generally because it requires at least 3 wires, and can only transmit 2/3 of the power of an equivalent 3 wire, 3 phase system.
Use VFD to make 3 phase from single phase source.
The electrical engineering 3 phase is calculated by mathematics. The total active power is equivalent to three times the power of an individual phase.
3 phase system has more power than a single phase system
Because 3-phase is the way electric power is generated, transmitted and distributed. The 3-phase format is broken down into single-phase supplies only at the consumer level, so that you might be on red phase while your neighbour on one side is on yellow and the neighbour on the other side is on blue. 3-phase is used all over the world for all significant amounts of electric power because it can be distributed using less cable and therefore less power-loss. Three single-phase supplies need 6 wires, while a 3-phase supply takes advantage of the phasing to use only 3 wires for the same power. Each pair of live wires acts as the return wire for the other wire in a symmetrical and balanced system.
You can get a 3-phase supply in most properties by negotiation with the power company, if your demand for electric power is high enough.