Debi,
No, rabbits don't get lonely. They have all sorts of fun by themselves!!

With a human to have, they really thrive alone.
No, rabbits don't really get sick unless you have a pretty intense setup. Just like goats, if you have several and are breeding, you will always have something come up, but generally speaking, rabbits are much less likely to get sick opposed to goats.
If the bunny has snuffles, that is a contagious bacteria like pneumonia that you really don't want to have if you are going to have breeding stock. The problem with snuffles is that it almost never is cured and generally always gets passed around to every single bunny,...meaning,..a problem with the herd that you can not cure.
If this would be a pet, it may be fine and some rabbits are just carriers, and do not have outward symptoms for a period of time. There are ways to treat rabbits, and with a good dose of med., a rabbit may stay asymptomatic for years.
As far as "buns", I have never heard of that, but I assume diarrhea is meant by that?
No, my rabbits don't get diarrhea. It's not common at all. It could be a sign of way too much hay,too much feed, or cocci, worms, or even entro(yes, rabbits get entro).
With this bun having snuffles and the poops, that tells me she's not in good health at all. I would be cautions.
If you are just getting one for a pet, I don't think any harm or foul is at stake. If it lives a great life without sickness, you're good to go.
Now, if you were planning to get more, or start a little herd, I wouldn't get one. Snuffles is something you don't want to start your herd with.
Bunnies are addicting!!! I have more rabbits than goats now! LOL!!