The eating grass part is completely normal. No one knows for sure why dogs do this, but most seem to, and prefer fresh grass. Some people have suggested it may be to aid fibre intake, but who knows.
Your dog may have food allergies, bacteria overgrowth in the digestive system, low digestive enzymes, or gastrointestinal parasites, or a combination of the above.
You can try over the counter Beano, probiotics, and a digestive enzyme. These are available at good pharmacies and health food stores. You can use an adult human dose and the frequency prescribed on the label.
If this is ineffective in controlling your dogs symptoms it might be best to try a prescription hypoallergenic or non-allergenic food.