To ask a factory to buy parts for you is always extreme high risk. Buy everything yourself from Mouser etc., that is the safest way.
Depends on who you're asking. I regularly do design with a local company; they are, in turn, part of a global CM. They have good procedures in place. For example, for a proto run, they only buy exactly what you specify (mfg+pn, if not supplier too). I have seen mistakes in protos, but they're more easily attributed to lazy employees than bad procedures or management I think. The managers are always interested to know about mistakes.
I've seen a couple of the failures shown above. Never seen a flipped chip. Have seen poor soldering, or missing paste. Usually they spot these and do rework. Most of the faults I've seen are either my fault (a poor footprint, in turn because the drawing is poor or I missed something), or avoidable with my help (e.g., ensuring adequate soldermask web width between pads, to prevent shorts on paste and wave steps -- closely spaced, untented vias is one I didn't expect to see, but it seems to happen regularly on lead-free wave).
I've also seen variable results, like the mfg cell nearby usually does nice work, while the one in the next state sometimes makes errors. So there's probably some variation in local culture, as well as employee performance. Which is probably about as good as you can expect.
Tim