for the permanent marker experiment i would use permanent marker to draw on some different objects with different surfaces and leave for a period of time and see if there are any signs of it coming off

and while im waiting for that, i'll draw a line on a piece of cloth with the same colour permanent marker and put soak it different solvents such as water, alcohol, vinegar, detergent and oil and if soaking doesnt work ill get a scrubber, dip it in each solvent and scrub and compare it to the original mark

lastly i'll do the same for a few brands and colours of the permanent marker and compare the results

for this experiment the independent variable would be the time and the different solutions and the dependent is the visibility of the mark
controlled variable would be the using the same permanent marker for each experiment, the amount of solvent in each cup, the time it is left in every solvent and using the same scrubber to scrub the mark

and all i can do now is hoping that Ms Zhang will approve of this...