Because both are the mid tower ATX format case, yes, you can move all into the Corsair Air 540.
And you only need i7 4790K and the z97 MB for games. The x99 + DDR4 are little bit expensive right now. Here is one of the review: i7 4790K and i7 5820K.
http://us.hardware.info/reviews/5599/intel-core-i7-5960x--5930k--5820k-haswell-e-review-8-cores-at-last
But if you real want the x99 + i7 5820K, may sure you will only use 2-way sli, because thr 5820K only has the 28 PCI-Express lanes. If you want more than 2 GPUs, then get the i7 5930K, which has 40 PCI-Express lanes.
One more don't buy the PNY SSD.
For i7 4790K
PCPartPicker part list:
http://pcpartpicker.com/p/FMxpRB
Price breakdown by merchant: http://pcpartpicker.com/p/FMxpRB/by_merchant/
CPU: Intel Core i7-4790K 4.0GHz Quad-Core Processor ($316.99 @ SuperBiiz)
Motherboard: Asus MAXIMUS VII HERO ATX LGA1150 Motherboard ($208.09 @ SuperBiiz)
Memory: G.Skill Sniper Series 16GB (2 x 8GB) DDR3-2400 Memory ($124.99 @ Newegg)
Storage: Crucial MX100 512GB 2.5" Solid State Drive ($180.98 @ Newegg)
Total: $831.05
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-01-28 12:54 EST-0500
For i7 5820K
PCPartPicker part list:
http://pcpartpicker.com/p/p6Vk7P
Price breakdown by merchant: http://pcpartpicker.com/p/p6Vk7P/by_merchant/
CPU: Intel Core i7-5820K 3.3GHz 6-Core Processor ($299.99 @ Micro Center)
Motherboard: ASRock X99 Extreme4 ATX LGA2011-3 Motherboard ($202.98 @ Newegg)
Memory: G.Skill Ripjaws 4 series 16GB (4 x 4GB) DDR4-2666 Memory ($229.99 @ Newegg)
Storage: Crucial MX100 512GB 2.5" Solid State Drive ($180.98 @ Newegg)
Total: $913.94
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-01-28 12:57 EST-0500