Go for one of the Asus ROG G750s. They are pretty beefy and a great desktop replacement designed for heavy gaming.
To answer your questions.. yes, they can be used to pretty much play heavy games all the time. They are sold as gaming laptops and being so damned huge and beastly, they are desktop replacements. Mine are.
They last as long as you care for them well. There is an old G73 in my household still powering on without a hiccup and it's quite a few years old. I actually still have an old asus F3 still going strong back from 2008/09. Look after it, clean it, don't use it as a frisbee and it will be fine.
The size of the screen won't affect the graphics card/performance at all, so it doesn't matter if you get a 15" or 17".. performance is based on cpu/gpu/ram/hard drive speed etc.
G750JH-T4074H i7-4700HQ, 32GB, 512GB SSD + 1TB , GTX780M-4GB
G75VW-T1013V
G74SX