It sounds to me as if she *could* have Sensory Processing Disorder. Those aren't quirks, but signs and symptoms of having sensory issues. They could be easily remedied by buying her clothing that doesn't have tags or buttons; turning her socks so the seams are on the outside or buying "seamless" socks; softer, more comfortable shoes or making sure that she can be part of the process in choosing her own shoes; no zippers or ruffles on her clothing, no high collars, buy cotton and nothing tight-fitting, no tights, nothing that could cause irritation, etc.
Sensory Processing Disorder is often paired up with another diagnosis or other diagnoses, though, such as Autism Spectrum Disorder or ADHD or other neurological disorder. Neither has to be severe or serious, just enough to "be on the radar."
Please remember that even if she doesn't have neurological stuff going on like SPD, ASD, ADD/ADHD, OCD, etc. she's still young enough to be in the "still toilet training" phase ok?
With the toilet paper, you want one that's soft but also absorbent. If that means spending a little bit more money than the tissue-thin stuff you can see through then spend it. We had issues even with the Angel Soft but my two girls that have sensory issues love the Charmin soft one. Just don't do Charmin soft and strong because it will clog your toilets like nothing else even with typical use.
Show her that she only needs a few sheets, and teach her to make sure that she pees completely before wiping or she'll have some leakage and think she's still wet... because she will be. Then teach her to dab and not rub in the front, middle, and back to absorb the pee. Dabbing will help with the sensory aspect as well as keep her from feeling raw and still wet.
EDIT: My street cred = three daughters including two that have sensory processing disorder... one having Autism and one having ADHD