OK, I looked at the last two pics, but am not sure what I'm supposed to be checking, especially in the next to last pic...Do you mean the clear barrier around the top of the tank? Is that the glass cover up you mean? Is it glass or plexiglass that's been siliconed(?) around the top? If your turtle can't somehow climb over it, I would think it would be OK. I know there must be one, but your turtle also has a UVB light, yes?
If you haven't, put the lights on timers. Clean the filter before you go and show your mom's friend what to if it clogs/there's a problem. I'd leave written instructions, for feeding as well. You can help control how much your turtle will be fed at a feeding (for pellets, anyway) by putting correct amounts into little plastic bags your can find in the craft section of Walmart (or similar place). Have a nice trip.

"You become responsible, forever, for what you have tamed." -Antoine de Saint Exupery-