Amy, being that he was about 10 weeks old, he should've been fine and healthy. Rabbits are resilient little animals, however they are more prone to illness when younger.
There are Alfalfa hay and pellets, and Timothy hay and pellets. Alfalfa hay and pellets should be offered to a rabbit at all times until they are 6-8 months old. This is because alfalfa contains more protein for a growing rabbit than Timothy hay and pellets. Once a rabbit is an adult, they should be switched to Timothy. If he did not have any alfalfa hay, then that put him as risk of getting a blockage, due to inadequate fiber in his diet. However, if he was pooping, then he wasn't blocked.
If his pee was brown, this is not normal. This could one of two things. Either it was blood in his urine, which would indicate either a urinary tract infection, or an internal injury. Urinary tract infections, while painful, are usually not deadly. And even so, they do not kill that quickly. An internal injury, however, is a different story. Internal injuries can be caused so easy in baby rabbits due to their small size. This can come from being handled or picked up wrong, and can happen without you even noticing. This would also cause blood in his urine, giving it a brown color.
The second possibility of the brown urine is, as you said, diarrea. This is more common in baby
rabbits, and can be very deadly. Diarrea in a small rabbit can be caused by internal or intestinal parasites, or a bacteria present in the intestine. The number one disease in young rabbits that causes diarrea is called Coccidiosis. It is very deadly if left untreated, and is usually a "silent" killer. It causes excessive thirst, swollen stomach (though sometimes not always noticeable, since it'll appear that the young rabbit is just growing up), and substantial diarrea. The diarrea will sometimes be so fierce, that it'll appear as liquid, just like urine.
If it was indeed diarrea, two other diseases that are also common in young rabbits are Tyzzer's Disease and Mucoid Enteritis. Tyzzer's disease is most common in rabbits right after they are weaned, usually within a few weeks. Your little guy would fall into this time frame. Tyzzers disease causes diarrea, which usually results in lethargy and dehydration. Tyzzer's disease is an organism caused by bacteria living in the lining of the lower intestines and colon. Tyzzer's disease is treatable only to a certain extent, as the mortality rate is around 90%. It's, unfortunately, a very deadly disease.
Mucoid Enteritis is another possibility which causes diarrea, and is common in rabbits around 4-12 weeks of age. However, this possibility is less likely in your little guy, since more symptoms are present than just diarrea. This includes a very swollen stomach which feels as hard as a rock to the touch, bad dehydration, lack of appetite, and a thick mucus in the feces.
As far as the bedding goes, I'm willing to bet that it look something like this:
This is pine shavings, which vary in size from maker to maker. Some pine shavings are thick and large, while others are as thin and dusty as saw dust. While pine shavings can irritate the lining of the lungs in small animals, it doesn't cause intestinal problems unless ingested. And if ingested, it will cause a blockage, inhibiting the rabbit's ability to produce feces at all.
Hope this helps!