I don't think it matters what kind of lotion you have to use, you should be fine. But just in case stay away from scented lotions
There is no age requirment, it's at the parents discretion.
HII,
I think 13 is the bit younger age for acrylic nails. The acceptable age is 16 years. Even this procedure makes the nail to go weak. She can have the nail arts to make her nails pretty.