Button Dropdown

Maybe I’m using the wrong term, please forgive me I’m new at this. I’d like to control the height of the dropdown, is that possible? I’m populating it with around 20 options which on a mobile screen doesn’t look quite right. I would love to be able to set a max height so it will scroll but it’s just not working out with anything I know as far as shortcode or html. I’m not very familiar with css so I’m not sure how to edit it or if there’s shortcode I can use. Any help with this I’d greatly appreciate.

Also, is it possible to add an icon to the dropdown button like you can to regular buttons?
https://www.themobileapple.com