If you're referring to the shoe version of a tabi, meant for outdoor use on their own, they're called jikatabi. They look like just indoor tabi (the traditional woven and sewn type, not the two-toed knit sock kind), but where indoor tabi have a woven cloth bottom, jikatabi have a tractioned rubber outsole.
The tie around the shoulders is called a tasuki. It's a sash or cord that's meant to hold the bulky sleeves of a kimono up and back while doing physical labor, so they stay out of the way and don't get dirty. Since Mai has no sleeves, it's purely a design element - there's no functional purpose for her to wear it.
FF9 cosplay? Hit me up!
2014: Anime Los Angeles and whatever else falls into my lap
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. Sometimes I use it.