1-you're also receiving IEV fault code. check both the control unit which sits atop the air box inner cover as well as the muffler valve for proper operation. i check both by removing air box outer cover and turning key on...then run switch to on and watch for proper cycling and cable movement.
2-tons of posts on here by very knowledgeable board members on inexpensive pump alternatives......less than 1/2 the price of dealer option.
3-i'm no ecm expert but not aware of any "limp-home mode" feature built into your ecm to compensate for loss of fuel pump pressure.
4-your 2010 has twin O2 sensors. front easy to access....rear a bit more work but do-able. if faulty they will dump code #13 into your ecm but i've seen contaminated ones cause your symptoms. sometimes a quick cleaning with toothbrush and sea foam or isopropyl alcohol restores their accuracy.