Sorry, you were sadly mis-informed. Science diet is now making crappy food unless you are feed the natural(that is the name). I would recommend feeding a good high quality food like Innova, Merrick (some really great flavors), wellness, ect.
If the pup vomitted just the once, and nothing else changed, I wouldn't be to concerned. If it keeps up, or the pup stops eating, drinking, etc. then I would seek a vet
No, science diet is not the best. I dont feed what most folks here find to be be great food, and I wouldnt even feed that, lol.
The throwing up of the grass is typical for dogs and once in awhile is normal for them to eat grass and vomit it.
The stool eating can be diet issues. They do sell tablets that you can give them that makes the stool undesirable to eat to them (as if it shouldnt already be....yuck) I have also heard that sprinkling some Accent...human food flavoring, on it will also deter them from eating their stool.
If there is more than ne dog in the house, you would have to out it in each dogs food.
If the vomiting gets frequent or he acts ill, then a vet visit will be the next step.