Heierthanu

I just got an 2005 allroad 2.7t for free...yes for free.
Put a battery in it and she started right up and drove her home. (It had been sitting for about 3 years since someone last drove it.) Did an oil change, spark plugs, and an air filter.

It has the following faults per the O'Reillys scanner (ordered an OBDeleven pro from ecstunning just hasn't arrived yet):
P0300: random misfire detected- pending
P0056: HO2S heater control circuit- Stored
P0036: HO2S heater control circui- Stored
P0141: O2 heater circuit- stored
P0161: O2 heater circuit- stored
P0491: Secondary Air injection system (bank 1)- pending
P0492: secondary air injection system(bank 2)- pending
P0305: misfire cylinder 5 detected- pending
P0174: system too lean- pending
P0306: misfire cylinder 6 detected- pending

If you clear the faults it runs great on first start up but as soon as you start it a 2nd time it idles rough and has low power. I ordered a timing belt kit and will be doing all of that soon but don't see that being related to any of the faults. Any tips on where to go from here or what to check would be much appreciated! Thanks!