To be honest a cheap filter is almost redundant in a turtle tank, you can get by without one if you feed her in a separate tub (their very messy eaters), and doing a small water change every other day.
Turtles, especially RES are very resilient, the red marks on her neck are her natural markings, under-coloured as a result of having no exposure to UV light..think of it as her tan

Its very normal for basking turtles to rub their eyes and scratch their legs as their drying out.
Enjoy your new pet
