Touching doesn't work, you need to swipe the page. This is really different than on a Kobo, but I hope you and your mother will get used to it. Since the Sony Reader has page turn buttons, some people prefer to use these and won't swipe a lot.
The main difference between the T2 and the T3 is the design and the resolution of the Eink screen. The software is almost the same.
You can sort your books:
- By Date
- By Title
- By Author
- By File Name
- By Latest Read
You can sort your books in collections:
- By Added Date
- By Date
- By Title
- By Author
- By File Name
You can add your series as collections via Calibre. Personally I wouldn't give the Aura HD away since it has an excellent design. The Sony Reader T3 is surprisingly lightweight. If that's possible where you live, I would suggest to have a look at this device first at a local store. You can take your Aura HD with you and compare the devices there.