My Gaming Build - Will it work? Could it be better?

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor (£87.00 @ Aria PC)
Motherboard: ASRock 970 Extreme3 R2.0 ATX AM3+ Motherboard (£69.20 @ Amazon UK)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (£48.36 @ CCL Computers)
Video Card: Gigabyte GeForce GTX 650 Ti Boost 2GB Video Card (£130.00 @ Ebuyer)
Case: NZXT Source 210 Elite (White) ATX Mid Tower Case (£38.64 @ Scan.co.uk)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply (£49.85 @ Aria PC)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer (£12.94 @ Amazon UK)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) (£69.96 @ CCL Computers)
Total: £505.95
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-09-04 12:37 BST+0100)

You have an alright build there, albeit a low-budget one. There are some areas where I would change things, but it would vary based on total budget.

To answer your questions:
That build could be improved in nearly every regard, assuming you could afford to spend more. If not, there are a couple of things I would tweak (4GB of RAM instead of 8 to afford a better GPU, SeaSonic-made PSU if possible, etc.), but it's generally alright. By the same token, it can be made cheaper, but it would vary by what resolution and settings you want to game at. That system is already rather low-end, so any cuts will cut directly into performance.
I would recommend the FX6300 over the 4100. It's only 13 pounds more at Aria PC, and it's a significantly stronger CPU.
That GPU will definitely not handle Crysis 3 on anything near high settings, unless you don't mind getting 30fps or less. It is, as said, a low-mid GPU, and there's only so much you can expect from it. Better cards made by nVIDIA include the GTX 660, GTX 670, GTX 760, GTX 770, and GTX 780.
1600MHz is generally the sweet spot for RAM. If it doesn't cost you anything extra it's fine to get faster RAM, but it's not worth spending more for.
Modular PSUs make for easier builds, though with a build that's on this tight a budget, I would direct funds towards stronger parts before I got a modular power supply. 500w is definitely more than enough for this build as stands.
I don't know that case, but in all honesty I'm just amazed that you found a case so cheap. If it looks okay (has a fan or two, no obvious major impediments to airflow) and will fit the components you want, I say go for it. More money for components, aye?
Win7 is generally my default recommendation, though I would recommend Home Premium over Ultimate, unless for some reason Ultimate is cheaper. Home Premium is all most users ever need, and usually the cheapest option.

@Marcopolo123: Your build looks pretty good, but you might want some RAM in there.

Generally speaking, 4GB is absolutely fine for gaming. However, budget allowing, 8GB is the optimal amount, and confers a degree of future-proofing.
Corsair doesn't actually manufacture PSUs, they purchase them from a number of suppliers. SeaSonic is one of these, and makes several of Corsair's higher-end units, as well as PSUs sold under their own brand, and under other brands such as XFX (which uses exclusively SeaSonic-made units). If it wouldn't increase costs too heavily, I would recommend using and XFX or SeaSonic PSU, as they are generally more reliable.
Now, not to disagree with the choice of the FX6300(heck, I recommended it), but those extra two cores aren't that big a deal. Games are usually optimized for four cores (making Intel's i5s the most ideal, but that's quite a bit more expensive), with higher core counts conferring less benefit. However, the FX6300 is a great CPU for the price, and definitely better than the 4100.
Wouldn't necessarily recommend those GPUs, just listing the nVIDIA options which were stronger than the 7790, as per your request. I would, however, try to fit in an HD 7850 or 650 Ti Boost, in your shoes, by reducing the RAM count. You'd see more benefits in gaming from a stronger GPU than a higher RAM count (within reason, of course).
Overclocking will increase performance, but every card has limits. As said, it comes down to budget and what you're looking for in terms of graphics.
Nope, 30fps was standard on the current-gen consoles, but that was one of their more archaic traits. 60fps will be the standard for all the new consoles, and there is a truly massive difference. To be entirely honest, I can't play at 30fps anymore, having played at 60. It feels extremely choppy.
Oh, there are a lot of traits in cases worth paying for. Cooling, capacity, and quiet being my big three. However, case is definitely not a high priority for spending.
1-3 fans is fine for a mid-end system. A 120mm at the front as an intake and a 120 or 80mm at the back as an exhaust is fine for most builds, and you're usually better off getting a better case rather than spending more on fans for a low-end one, due to higher-end cases having superior fan quality and airflow, thus allowing them to cool more effectively with fewer fans, which in turn allows them to be quieter.
Wow, that's a pretty amazing deal. I'd have to pay three times as much for Ultimate as for Home Premium.