Wow.. that's some list. As your aware gaming is so subjective and what one person likes doesn't necessarily mean others will too. Take a look at this site which allows you to download a demo to see if you like the game or not plus it's free too...
Steam is a gaming client that has a list of games categorized by gender, price, publisher, and ratings. If you are absolutely not sure about the type of games you will be interested in Steam is the way to go. Search for single-player or if you prefer find a good multi-player game. Start out by downloading free-2-play and Demo versions, then move on.
Well it should be okay for the most part... although stuff that is graphically demanding will probably cry out in pain on the nvidia 520m gpu it has... that said it'll beat the performance of laptops with crappy IntelHD gpus, it should be fine for basic console ports and older dx9 games (provided they are set to LOW detail settings as it'll be like a slideshow on Medium/High), and all web browser type games.
As the 520m has only 48 cores it'll be around a spec of a 7 year old desktop GPU like the nvidia 8600, so you can see why it's not going to perform well for modern games.