Got a Prodigy myself, if you have any questions then give me a shout.
Would a 30mm thick fan fit in the front intake?
Yeah pretty sure. Using a Bitfenix Spectre Pro 200mm (which is 25mm deep) myself and while it looks fairly snug in my case I've seen people using the Spectre Pro 230mm (which is 30mm deep).
I'd strongly recommend double checking (and triple checking) how compatible that motherboard is with the Hyper 212 Evo. If you've done this I apologise, it's not a motherboard I'm very familiar with and at a glance it looks very tight.
On PSUs you are slightly length limited. I'd normally suggest the Rosewill CapstoneM or XFX Pro XXX series, but they seem a little long.
Antec HCG 620M looks ok as does the Seasonic M12-II 620, I'm struggling to find many that are under (or close) to the 160mm limit. You can probably exceed that by a few mm if you are confident you can get the cables to bend around, but that would be more of a worry with a modular PSU. You might have more luck looking at slightly smaller capacity PSUs, like Outlander said you don't necessarily need 650W+ unless you have some sort of unusual plan (it's not like you can really cover for SLI on an ITX build) 500-550 PSUs might be that few mm shorter.