You can’t style options, as they’re browser-dependent and there isn’t an agreed standard. You’d have to use a replacement, which provides the functionality with other components.
Then, to keep it open, you should be able to toggle classes and states in the inspector. I’m Firefox, it’s above the style inspector, labelled as .cls and :hov, I believe (I’m on mobile at the moment).
You can a bit, but that will be limited and will differ by browser. Look at something like this to do it: https://medium.com/@ross.angus/styleable-select-box-replacement-in-pure-css-and-semantic-html-1f38a400b285