Upgrade Studio XPS 435 MT Video Card--Need Opinion

I have a Dell STUDIO XPS 435MT.  So far, it is the standard issue, but it's time to upgrade.  I just ordered a 750w power supply, and I need a new video card.  I want to install the GIGABYTE GV-N760OC-4GD GeForce GTX 760 4GB (http://www.newegg.com/Product/Product.aspx?Item=N82E16814125470), but I'm concerned about two issues:

1)  The width of the new card matches the space I have in the computer tower.  That seems fine, but if the new card fits exactly, will the fans work efficiently with little to no flow on the bottom of the case?

2)  The card is huge!  I have plenty of room for the massive 11.5 inch long card, but what about the clearance with respect to the plugs at the bottom of the motherboard?  Will the size of the card block the area where the plugs connect to the base of the motherboard?

I am hoping that someone has experience with this card/installation.  Any help or advise is GREATLY appreciated!

Shawn