Why all of my games run slowly when the charger is not put in the laptop .. but when I put It .. the games wor?

Because a laptop requires a lot of power while running games and laptops battery doesn't provide sufficient power but when you connect your laptop with your charger then sufficient power is provided to your laptop for running games.

the charger or adapter can give it extra power to run things more quickly, and boosts the computers performance and maintains it, and sometimes, with out it, it loses power and slows down to save power. Some computers do that, while others just use the power at max when the chargers gone and dies out quickly.

To save power when the charger is removed the laptop graphic card (Mostly Ati one) go into power saving mode from performance mode. You need to fiddle around with graphic card settings and power setting in windows control panel to disable that. I have an HP dv6. with ati card in it. In ati driver options it has an option to disable this feature. Though i must warn you that this will shorten your backup time drastically. When I play GTA 4 on my laptop without charger it only run half hour to 40 minutes maximum.

Of course they will, the computer is running on reduced power, to extend the battery life. Go into Power Setting, and look around. If the power setting are user adjustable, then they will not harm the machine, will they. You do have to do SOME thinking.

just change the performance option when you're on battery. click on the battery icon in the bottom right of the screen and select high performance. Changing the performance will NOT harm your laptop; it will just drain more power from the battery.