Is it possible to charge car battery through cigar lighter socket?

Yes, it is possible to charge the battery through a cigarette lighter socket, but there is a couple of caveats:

1. The car's circuitry must have the lighter socket "live". It may require setting the ignition switch to "accessories."

2. The charge rate must be kept low enough not to blow a fuse associated with the lighter socket (often 10 Amps). At 10 A it is going to take several minutes to get a depleted battery charged enough to crank the engine successfully.

There are commercial products that work on this principle.

However, it seems you do not so much want to charge the battery but to keep it charged while running electrical devices. This is possible, but the 10 A limit means you can not go over 135 W of sustained total power draw without depleting your battery.

The air conditioning compressor is driven by a belt drive from the engine, so you cannot run that from a purely electric source. There may be AC compressors that are powered by AC electricity or by the engine.

The blower that circulated the air is electric and can be powered from the battery. The dashboard is mostly electric, the only bits I can imagine being of use in a stationary vehicle are the entertainment system and the clock. They can be powered this way.

You are not going to be able to power the accessories through the cigarette lighter like you are suggesting. The biggest issue would be you would not be able to provide enough power through it to replenish what is being drawn from the battery.

A much better idea is to attach permanent leads to your battery which you can access easily. This will allow you to supply the power to the vehicle which will not allow the battery to deplete.

Even another idea is to install a separate deep cycle battery to provide the juice to the accessories which you want to run, yet will be completely autonomous from the main vehicle battery. This way you will never run the risk of the vehicle being stranded due to over use of the battery. There are several different products on the market which will do this for you (they may or may not use a deep cycle battery, but will use a dual battery setup). You might want to check out this thread and see if it helps.