Does running your graphics card on maximum resolution in games increase wear and tear on the graphics card?

No necessarily. Not unless you Overclock your video card, it will definitely increase the wear and tear of your graphics card. Video cards nowadays can take more punishment, just make sure you have the proper cooling and ventilation. Keeping the fan speed of the graphics card to 60% and up works wonders.

yes if one the game is resource hungry like call of duty or crysis it will heat it up a tremendous amount a fan will help significantly nad using a graphics card without a fan not built on to the card as well

Heat is the killer for video cards, search 'NVidia heating problem'. While more recent chips do indeed run hotter, they are better able to withstand it. Your card's fan is the critical moving part. If it fails, you may not notice until it is too late.Too late happens when it fails. I regularly inspect and clean out the dust around the fan and housing using compressed air. I also check to see that the fan moves freely, people tend to forget this one as it will point out a sticking fan quicker. The card has a rated resolution range and running it inside those confines should be fine as long as you aren't running it overclocked. Individual differences between the various components can also add heat. Overall you should be OK to run at maximum. Good luck.