That's schematic of half adder using only NOR gates.
Why aren'y inverters used?
In the picture, there are 2 NOR gates where the two inputs are same as A or B.
Why don't we replace these with a NOT gate? Is it because their oparations are the same as an inverter and a NOR gate needs 2 CMOS, but an inverter needs a CMOS?
Are there any problem in fabrication or entire operations to replace those?
Yes, you could replace those two NOR gates with inverters.
You could use inverters from a 74HC04, and NOR gates from a 74HC02, for example. But you may want to use only 74HC02 packages, for some reason. Their behaviour would be identical, except for a slight change in propagation delay.
If you were implementing this adder unit with MOSFETs in an IC, it's certainly easier to implement inverters than two-input NOR gates with their inputs joined, so from that perspective inverters make more sense.
Otherwise, if you have a bunch of unused NOR gates, then it makes sense to employ them, since they're already there. Likewise, if you had some unused NAND gates, you could use them in the same way, with joined inputs, to form an inverter.
Everything depends on what you have available, and what is easier to implement. Also, if speed is an issue, then there's a tiny change you can make to gain perhaps a nanosecond:
simulate this circuit – Schematic created using CircuitLab
By tying one of the NOR inputs (G2 and G3) to logic low (ground, 0V), you still have an inverter, so logical behaviour has not changed. However, because the sources of signals A and B are driving one fewer gate inputs (two instead of three), they have less capacitance to drive, and will transition between logic states slightly more quickly.
If you have some spare NAND gates, from a 74HC00 for instance, here's how you might use them in place of G2 and G3, and still have exactly the same logical behaviour:
