I've been trying to do that for the last 5 years, but what puts me off is the availability of cheap ready made inverters which are so cheap and they have options I can never dream of doing like them in a long time. You can never compete with industrial types unless you want to do it for educational purposes.

You need a DC link filter with over voltage protection due to the Back EMF generated from the motor. You also need a circuit to put a resistor in series with the DC link capacitor at start up to stop it from tripping the main circuit breaker for 1 to 2 seconds for the dc link capacitor to charge up then bypass this resistor. You might also need to add power factor correction circuit before the inverter.

You need to add dead time control for your gate drive signals which will consume all the resources in your 8052 leaving no time for the rest of the control functions.

Yes you can do if you use DC to DC converters to step voltage up from +5VDC to +15 VDC but it is not preferrable and costy because you need about 2A of gate drive supply to be able to charge the gate capacitance of IGBT to switch it on at hi speed. Use a dedicated isolated gate drive supplies or one supply and use the bootstrap method of driving the IGBTs.You also should think about making the off voltage to the gate of IGBT to at least -8VDC to make sure that the IGBT is off because of high speed switching at high VCE a voltage spike would pass through the intrinsic collector gate capacitance Cge which tends to keep the gate at positive potential and keeps the IGBT on, this will be offset with the -8VDC which makes sure the IGBT is kept off.

Yes you can use discrete IGBTs or IGBT modules and in both cases you need to worry about protection circuit and thermal management.

You need to separate the high current high voltage circuit from the low voltage circuit.
You also have to make the tracks from IGBT driver to the gates a minimum in length. Most decent manufacturers connect the gates of the IGBTs to the PCB directly through screws or by soldering. If you have to use wires make sure they are twisted pair and no more than 5cm in length.
All other standard PCB tips should be used including solid ground planes, ferrite beads, varistors and fuses and short circuit and over voltage/current protection.
As Erik mentioned an 8052 is not powerful enough to make an inverter because there are alot of strict timing requirements for gate drive that require dedicated hardware for 6 PWM outputs and powerful processor to do sophisticated math functions to produce Sinusoidal PWM.
Mahmood