Hello!!
While I am not an expert on the other issues on your machine, I would recomend a wipe and a clean reinstall. Those root files with the random characters are what an asian language font typing system rendered into the standard qwerty would look like (lots of experience). My quick gut instinct tells me that the language used was either Korean or Chinese but there is no real way to tell except to type those letters into their language and see what you get as rendered words. With the additional context of the files being in root and being excutable my guess is they were going for full remote access. Unless you want to spend a large chunk of time and energy combing through your entire system resecuring it, a reinstall would most likely be faster and more thorough and far more secure. Just my two cents.
Cheers!!