I've done that before. Not in batches like that, but like I've hatched chicks, and then a couple weeks later I would add a few new chicks. But I'd leave it at that. Adding too many new chicks to your batch *will* cause problems to the younger ones, like pecking and things may get kinda rough...
I mean, maybe this is just me lol, but I usually don't worry too much about the chick's poop unless they're really acting sick. Just with say, goats and kittens, their poop is usually a little watery or diarrhea-ish for a while. Keep the electrolytes going, and make sure to TRY to fed them...
It was our first time incubating about 2-3 months ago and it was (not gonna lie) pretty stressful. Maybe it was just because it was our first time, and our humitity was all weird, but it was still pretty stressful. Personally, especially because you would have to hand turn them, i wouldn't go...
I honestly don't know what to say, because there are at least 100 chicken deseases, including chick deseases. I think that just feeding electrolytes, giving medicated feed, and some TLC is the best you can do right now. I'm not completely sure though, maybe someone else can help a little more...