yes all things plugged in make your bill high when they are on. but a test i did in school so the cost is a little out dated but leaving a 100watt light blub on for a 24 hour period only cost about .03 cents a day. so in a typical 30 day month that light would cost less than a dollar. as i say that was with electric price 15 years ago so it might be as high as 3 dollars. i would imagine a pc in sleep mood on all month is about 15 dollars in not less i mean me using a space heater to eat one of my bed rooms all month only added 15 dollars and it was using more juice than a lap top.
Yes, you are better off turning your laptop off completely or hibernate it so when you turn it back on, you do not have to restart your laptop. Also, if you are not using your laptop, unplug your cord from the power point as this is costing you money.
sleep mode still needs power though not much. And yes it it charging you. Wise way is to really turn off any electric appliances when it is not used. Avoid putting them on stand by mode (usually TV and PC)
so i just turn them off "shut down button"