Women's Play Short Rain Boot

Do these boots run big? I bought a pair in my usual size, but returned them because they were too roomy. Should I buy a size down?

Ordered an 11 women’s Hunter boot for wife’s bday. Disappointed to receive a sz 5. Will return, but skeptical to reorder! Can you guarantee?

If the “M” indicates regular width, what is the number only size indicate?

I have wide feet, will the medium still fit if I get the next size up?