i would suggest giving them a bath with warm water and Dawn dish soap to help clean off any potential bugs they could have, i follow up with a rinse of apple cider vinegar and a final wash off with just water-seems to work for mites/lice. check over their feet for any irregular bumps in the leg and foot scales-that could mean scaly leg mites, but if they are young they may not show signs of them yet. if you see raised scales you can treat with a few different items, i've been hearing WD40, Pam cooking spray for those with foot feathers (not sure this really works yet, but i'm trying), you can give them a foot bath of alcohol and then cover with Vaseline or PulVex, or i have also read you can use Nu Stock made for horses/dogs/cattle and can be found at the feed store-looks to be about $15-$18 per tube.
if they are not sneezing/coughing/gasping for breath or have any mucous coming from their nostrils or mouth i would not worry about them being sick. there are many different forms of poop that a chicken could have, and many are not serious but look really gross! this will be helpful while you get used to having chickens
http://www.chat.allotment.org.uk/index.php?topic=17568.0
roosters are not always a bad thing to keep around if you are allowed to have them on your property! many will see you as the flock leader and will leave you alone. but you will need to ack like the roo yourself! i am not sure how BO roos are on attitude towards humans touching their girls but the roos i have seem to just watch me and wait for food or treats. i may get an occasional wing dance but that gets stopped when they see a girl cross their path!
eta: after the bath don't forget to blow dry the birds off! they need to be kept in a warm area till they fluff back out too! (usually a few hours till they are oiled again and ready to go out) i would de-worm the chickens with something-either use pumpkin seeds and a mix of minced garlic as a natural remedy. pumpkin seeds will paralyze the worms but not kill them, garlic will help kill the worms and should help keep them clean of the internal worms and biting bugs. there is not much on the market i have seen that can be used with chickens being kept for egg laying that you do not have to toss the eggs for a few weeks, so using the pumpkin seeds i have found very effective for finding out if they have worms before going onto something more effective but needs a withdrawal period.
i also wouldn't be too concerned with the brahma being picked on, if all birds were raised together they are usually fine. that roo may have been picked on by a bigger roo or older hens that were establishing a pecking order on him.
good luck with them!