Looks more like a red sex link than a rhode island red, they go by many names, cinnamon queen, golden comets, ISA brown, red star, golden buff, etc. depending on where they come from. Rhode island reds are more mahogany colored.
She also looks like she has feather damage on top of her head behind the comb also, that could be rooster damage. If she was in crowded conditions then she may have been feather picked where she was. If you haven't done so already, I would give her a good going over to make sure there are no lice/mites (link below).
The wet, dirty rear is most likely from runny droppings, that could be from dietary changes, drinking lots of water, or possibly internal parasites. If you have a vet that will do a fecal for you, that will look for that. If not, since she's a new bird, I would consider worming her to be safe. You can use Safeguard Liquid Goat wormer (that is usually the easiest to find) and give her .23 ml per pound of body weight orally once a day for 5 days in a row. You can get a weight with an inexpensive digital kitchen scale. Shake the medication well before drawing your dose, it settles out. Hold her or wrap her in a towel, pull down on her wattles and put the medication in the front of her beak 1/2 ml at a time and let her swallow (reduces risk of aspiration) and repeat until the entire dose is given.
The feathers may not fill in until she molts.
https://the-chicken-chick.com/poultry-lice-and-mites-identification/
