In general I recommend dual labelling for pickers, with a fixed, permanent category prefix outside the form itself - in your example, that would be 'Fee Option' - and a dynamic status label inside the form to indicate its current status. Think of this as a call-and-response or question-and-answer scheme; "Fee option?" - "Monthly | Annual | Lump Sum"(or ...
I would say it depends on what the interaction is. Looking at Google and how they implement Material Design we can see that the "placeholder" value is actually the name of the input label. So in your example it would be: "Fee Option".
But generally I would say it depends on how the overall design is and what type of user interaction you want to have.
I wouldn't recommend the 'x' icon, because it breaks with conventions. An 'x' typically closes a window or container (e.g. makes it vanish), so user might get the impression that the whole dropdown would be removed when clicking on that 'x'.
However, up and downward pointing chevrons are associated with expanding/collapsing content in the given direction, ...
My best experience with a similar select autocomplete field looked like search but works as a select and I can type to filter.
Se on the example:
No limit, no need extra information, no need trial.
The user can just start to type and will find what they are looking for.
On item 2 you can show all options order by name without filter and as soon as the user ...
It's not really a problem if the list still contains a lot of items. But for such a long list of entries, i would definitively recommend a form of searching.
Here are some plugins that may be what you are looking for:
As others have said, that control looks like a button, so users will expect to click it. Adding hover effects will only reinforce that expectation.
In any case, I would be wary of using hover to expose this information, for a few reasons:
Hover is not a thing on touch devices, so anyone on a phone, tablet, or touch-notebook won't be able to access it.
I believe that you already know it but the element just could look like a button if it is a button and this is not the case.
I would like to see more than the buttons, I would like to see where and in which situation you are implementing these elements. Is difficult to give you a good answer without this.
Otherwise my viewpoint you have 2 alternatives:
"Faded" suggests greyed out/disabled, so is less likely to suggest clickability than "highlighted", which is what your buttons show.
However, hover styling may be appropriate to draw attention to the tooltip; possibly setting the background colouring or border of the selected summary element the same as the tool-tip to produce a visual connection between ...