Why would this girl call me Hun darling and babe an I don't know her that well, might she have a thing for me?

Some, typically lower class, females use the words "honey," "hun," and "babe" like guys use the words "buddy," "bud," and "bub." It's just a way of addressing someone they don't know very well. Means absolutely nothing other than "this girl" is probably not very educated or refined.

People who use pet names generally use them on everyone

Judging by your confusion, you're most likely a prude that is afraid of relationships. She called you hun because that is her preferred word to address guys. OK, hun?

She doesn't know,

or

maybe she doesn't care to remember

your name.

Yeah, but probably not the way you think. Girl's affections that appear out of nowhere are usually attached to a shitstorm.