This is the case and psu right?
It should fit yes seems like the pc will be functional if not a little tacky with the blue leds everywhere and blue highlights on the case. Don't get me started on the led fan in the PSU.
Sure the LEDs will look cool for a little while but they will soon be annoying after a while, hopefully the case has some sort of led on/off switch. If not you can easily clip out the leds from the fans for a more subtle looking PC.
Aesthetics aside, I think the only issue with the case is going to be cable management if the PSU is not modular. You have no easy way of routing your extra unused cables out of the way to the rear of the case due to design. So you may need get creative and zip tie your extra cables and tape them to the top of the case or stick them in your optical drive bay area.
As for the 8 pin thing,
On the topic of that converter - Yes, it will work fine. I'm not 100% sure but I believe the extra 4 pins are typically for extra grounding, not so much extra power. Based on what I've read, people have no problem even overclocking with a 8 pin mobo to 4 pin PSU design.
Pretty much what he said.
8pin power not really needed unless you're going to be doing extreme sub zero temp overclocking with dry ice, liquid nitrogen, liquid helium..
It does provide more power but it depends on the PSU. PSUs will real certified 8 pin cpu power, will have 2 ground and 2 power cables to each 4 pin connectors.
The adapter is simply a placebo.