Odd Mobile Display Issue

Hi,

1. They don't do the same thing. One makes a copy of the product entry in the wishlist to the cart, the other moves it. Which means that when you move the product to the cart, you loose it in your wishlist. That's why you have the to buttons.
If you only want one, you can always use CSS to hide the one you don't want.

2. You can have several wishlists and thus that button is to move the product to another wishlist or a new one. I don't see why you say it's redundant ? Redundant with what ?
If you don't want it, you can hide it with CSS, and if you want to change the text of the button, you can use a translation override:
www.hikashop.com/download/languages.html#modify

3. The fact that these buttons display differently from the others is because you're missing some CSS. As we told you before, you're using custom CSS from an old version of HikaShop and thus, you don't have all the new CSS that we had to add for the new things we've added in the frontend. And these "dropdown" buttons are part of the new things we've added.
So it's not from the template but from your old custom CSS file of HikaShop frontend default. If you switch to the default CSS of HikaShop, you'll see that the buttons display just fine, like it does on our end.