best is not to charge when using, and after charging it full, unplug it. My macbook air battery life used to last twice as long. I've been leaving the power cord while charging and after its full. But thats after using for 3++ years with 300+ charge cycles already, so may be just the battery dying.
Better safe than sorry.
No it doesn't work this way. When the Lithium "Hybrid" Polymer, not Ion cells are charged, power supply to the equipment is another circuit. It is not as if the charger to charging the battery and the equipment is consuming from the battery at the same time. It don't work this way since th incoming voltage from the charger will be at 4.2V per cell. You can't have current flowing into the cells and have the current also flowing out the cells at the same time.
Battery will degrade regardless you charge it or not, that's the technology for Lithium based battery. It is even more pronounce for Lithium Hybrid Polymer, which is what Apple laptops are using. Older laptops uses Lithium Ion which are more durable. Lithium Hybrid polymer are chosen for their higher discharge rate and also their flexibility to shape into various dimensions.
However the more your discharge and charge (one full cycle) of your cells the faster it degrade, that's the usual wear and tear imposed on the chemical. Basically the polymer instead crystallise and inhibit the flow of ions within the cells.
Leaving your power cord to your system will not cause your battery to degrade or over charge. Lithium Ions and Polymer are not your usual NiMH or NiCD, you can't overcharge it. It will bloat unusually and either catches fire or burst into flames. That's why all Lithium based batteries require sophisticated Battery Management System(BMS) to ensure no overcharge or over consumed. Lithium battery are charged at 4.2V constantly. Full current is pump into it until towards the end where trickling charge is used. It's different from charging other batteries type using elevated voltage over time. Lithium Based battery must not discharge below 3V or the chemical will go into an irreversible state and can't be charged. The nominal voltage is 3.7V after charged.