Can I use a 240v to 120v adapter to plug my 230v window air conditioner into a normal wall outlet without having loss of power to the unit or without potentially facing any other problems?
So you have a 120V outlet on the wall, and a 230V air conditioner? If so, then probably not. Those "adapters" (assuming the kind used for travel) are intended to power SMALL appliances, like shavers, cell phone chargers, MAYBE a hair dryer. An Air Conditioner likely requires WAY more power than those devices are good for. That's why it is designed for 230V; it is too much power for a standard 15A 120V outlet.
But you can check to make sure. Look on the nameplate of the Air Conditioner for the wattage. A standard 120V 15A outlet is good for 1800W maximum, assuming a "non-continuous" load and NOTHING else on the same circuit. But worse than that is that most of the travel type power adapters are rated for 1300-1400W MAXIMUM. If your A/C unit draws more than that, then it can't work without risking a fire.
As the others have noted, these converters are not rated for this kind of use. Even if they were, it still wouldn't work. Because the voltage is halved (approximately), you need to double the current to get the same power (wattage). So your 15 amp 230 volt AC is going to draw 29 amps. Even if we assume 11.5 amps max, the draw at 120 is 22 amps. Household 120 volt circuits are limited to 15 or 20 amps so this just doesn't fly. Add to that an A/C unit is considered (I believe) a continuous load and therefore, you must derate the wiring current capacity to 80%.