Here's a link to the Scoop on Poop FAQ which might help, scroll down to get past the new born poop post:
https://babywhispererforums.com/index.php?topic=157413.0Oats are whole grain but I can't say I know why they tend to be more acceptable for babies than for instance wholegrain pasta or brown rice, perhaps because the grain has been processed/rolled - sorry I can't expand on that. There is no harm in holding off from oats/grains for a little while yet though as your LO is only 6 months, you might find it more suitable to stick to veggies and some fruits for now and re-introduce grains in a month or 2.
Very small amounts of whole grains are usually okay unless LO reacts negatively (ie too full for other foods or milk) for instance we always had shop bought whole grain sliced bread and I didn't switch to white bread for DS as it was too much of a hassle to buy another loaf for the small amount I would give him, say a quarter slice and not every day, but I used white pasta and any other baked/bready things were white (pitta bread, bread rolls, naan, scone, pancake etc).
It's very hard to advise on poo - it is expected to change when they start solids, LOs are expected to put a lot of effort into it because they have to learn to use their muscles to push, but constipation needs to be avoided. My DS had some constipation meds for a short time, the doc actually gave me a huge bottle and told me to use it daily on-going but after a little while I saw the health visitor who advised me to stop because she said babies on meds for long periods do not learn to push properly which can cause problems too.
Another thing I have always felt is that offering only one food at a time can cause more problems than it avoids. For instance if I had done the 3 day thing with carrots for my DS he would have been totally constipated, but offering a wider variety of foods and not the same/single food every day meant he had more chance of the foods balancing each other out - and that goes for foods which made poo too soft as well as foods which made it too hard. Some foods effected his reflux rather than his poo, eg pears but he could have grated pear made into little pancakes and was fine. The general advice these days is that you don't need to trial each food on it's own unless there is known allergies in the family or LO shows allergy/intolerance in which case you'd need to reduce the variety so you could more easily identify the problem food.
Sorry I don't have a straight cut answer for you. If ever in doubt it's best to speak to a health professional.