I guess a towellette is a small towel one make wet before cleaning your face or your hands with it, example before or after eating in an airplane they are often "served" hot and with an odor of lemon! They are very comfortable and makes you feel relaxed and fresh after use.
No, it means one of those wet wipes, fresh wipes, I'm not sure what you call them.
I have no idea. This is not an English word. It may be American but it's a complete mystery here in Europe
I realize this is mostly marketing, but "moist towelettes" is probably the preferred term, since it generally refers to those things used on face or hands. "Wipes" is a term generally referred to as those things used as toilet paper, either for babies or adults. Again, just saying what marketing firms call these things.