Would the size 6 in big kids fit me since I’m a 6 in adult?

The Big Kids size 6 would be too large for you. I wear a women's size 6M shoe and have purchased several of these particular UGG slippers; the Big Kids size 4 are a perfect fit for me.

Are these really narrow for women to use??

I don’t believe so because my granddaughter has a wide foot & fit her perfectly.

What is the difference between a little kid size 3 and a big kid size 3?

Look at the age guide. Big kid 3 is for a much older kid. My 7 year old wears the big kid size.

Bought these recently for my daughter and she used the ugg cleaner on them and the texture changed. Is there any kind of warranty?

You may need to check the cleaner that was used. If it was not a designated brand that they recommend, they may not warranty it. You may need to contact them. There may also be disclaimers on the UGG cleaner but you should be able to contact them directly.