I wear 11 what should i purchase 11 or 11.5

I wear a 12 in other brands (including Keen sandals), but when I bought this brand in a 12 it was one to two sizes too small. Based on this, I'd say if you wear 11, purchase 12 or 13.

Can you wear these in water without ruining them?

I wear mine all the time when putting my pontoon boat in the lake and never had a problem with them yet. Very comfortable and when these ever wear out I will buy more

Are these men's or lady's? Description says both. I won't matter except sizing will be different.

I think they are advertised as "men's" only because of the colors offered. To me, they are unisex but you just need to figure out the correct size if you are a woman. I am a woman and have bought a couple of these types of shoes specified as men's shoes. I typically wear a woman's size 11 and a size 43 (US men's size 10) in these types of shoes seem to fit well. My bare foot measures approximately 10.5 inches. I'm stuck buying men's because the shoes advertised as women's, which have more girl colors like hot pink, purple, etc, stop at size 42. If the company that makes these types of shoes reads this, please make available a large size range of shoes in girl colors. We all don't have tiny feet...thank you