DC

temps looks fine to me, just like for school use, browsing internet or using docs, temp is around 40 to 45C
When I game, it is around 70 C so I don't think fan is bad

Quick Sync worked! 

I looked it up at amazon and shipping costed more lol

I actually have done the #4 for few months. It was really bad. Thanks for suggestions 1 to 3. #4, "fuck it"! LoL

On the Newegg, I found this corsair builder 600w 80plus bronze atx psu. it is 57 dollars and it has 20 dollars mail in rebate. Is this a good quality psu to buy for single gpu gaming pc?

Cxm450 and 550 were like 5bucks difference so I chose 550

I will try to send them for counseling together or at least individually 

ok Thanks

Nope, it doesn't matter at all
 

Yes it is compatible. 

Yes HDMI into the graphics card. And Newegg has a great video on installing Windows and final touches.  The process might differ a little because the video is 5 years old but it should be fine.
 

That CPU is lacking, if you intend to stream get at least an i5. Otherwise you'll be ok with that PSU but I'd advise, if you plan on upgrading anytime soon, getting a better one. 

you should be good with that power supply, as for getting a cheap cd/dvd drive I would recommend just searching amazon, there they are a dime a dozen.  

Option one:
PCPartPicker part list: http://pcpartpicker.com/p/NLYZkL
Price breakdown by merchant: http://pcpartpicker.com/p/NLYZkL/by_merchant/
CPU: Intel Core i5-6600K 3.5GHz Quad-Core Processor  ($245.99 @ SuperBiiz) 
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler  ($34.50 @ Newegg) 
Motherboard: ASRock Z170A-X1 ATX LGA1151 Motherboard  ($92.98 @ Newegg) 
Memory: Avexir Budget Series 8GB (1 x 8GB) DDR4-2133 Memory  ($29.99 @ Newegg) 
Storage: A-Data Premier SP550 120GB 2.5" Solid State Drive  ($38.99 @ Amazon) 
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive  ($46.89 @ OutletPC) 
Video Card: PowerColor Radeon R9 380 4GB PCS+ Video Card  ($188.89 @ OutletPC) 
Case: NZXT Source 210 Elite (White) ATX Mid Tower Case  ($41.99 @ SuperBiiz) 
Power Supply: EVGA 650W 80+ Gold Certified Semi-Modular ATX Power Supply  ($69.99 @ Amazon) 
Optical Drive: LG GH24NSC0B DVD/CD Writer  ($13.99 @ Newegg) 
Total: $804.20
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-03-06 17:07 EST-0500
SSD, $4 over budget.
Option 2:
PCPartPicker part list: http://pcpartpicker.com/p/BCKTXL
Price breakdown by merchant: http://pcpartpicker.com/p/BCKTXL/by_merchant/
CPU: Intel Core i5-6600K 3.5GHz Quad-Core Processor  ($245.99 @ SuperBiiz) 
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler  ($34.50 @ Newegg) 
Motherboard: ASRock Z170A-X1 ATX LGA1151 Motherboard  ($92.98 @ Newegg) 
Memory: G.Skill NT Series 16GB (2 x 8GB) DDR4-2133 Memory  ($59.49 @ Newegg) 
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive  ($46.89 @ OutletPC) 
Video Card: PowerColor Radeon R9 380 4GB PCS+ Video Card  ($188.89 @ OutletPC) 
Case: NZXT Source 210 Elite (White) ATX Mid Tower Case  ($41.99 @ SuperBiiz) 
Power Supply: EVGA 650W 80+ Gold Certified Semi-Modular ATX Power Supply  ($69.99 @ Amazon) 
Optical Drive: LG GH24NSC0B DVD/CD Writer  ($13.99 @ Newegg) 
Total: $794.71
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-03-06 17:08 EST-0500
No ssd, but 16gbs of ram, under budget.

http://pcpartpicker.com/p/zD2TXL
$340 roughly,