The sound at the start of the video - I can't really determine whether anything is abnormal there. Could just be fuel injectors pulsing.
What I can help you with is the second sound that you refer to as a scraping sound coming from the passenger side/belt area of the engine. I had that exact same sound on my 2011 Si. I originally thought it was a bad bearing in the drive belt tensioner. After doing some research and reading, I was able to isolate the source to the PCV, which is located very close to the drive belt pulley.
Here's a video I found that shows the location of the PCV on the Si:
http://youtu.be/KSACyskPtKo
Find the short hose that runs from the PCV valve and pinch it. The noise will go away if you pinch firmly.
I ended up replacing the PCV valve and the little hose. Noise gone, and you're out about 30 bucks in parts. Easy to replace, too.
You need:
17130-RBB-A01 VALVE ASSY., PCV
17131-RRB-A00 TUBE, PCV
94109-14000 WASHER, DRAIN PLUG (14MM)
Just reuse the two hose clamps. I replaced the PCV valve, but if you want to spend as little as possible and don't mind a possible return trip to the parts dept, try replacing just the tube (hose).
