Hello Colten,
Thanks for reaching out to us! Let me help you with your questions.
Check out our demo site here, I’ll be referring to this in my answers.
show a search feature
That is absolutely possible even with the free core The Events Calendar plugin. There is a search bar like this appearing at the top of the calendar:

a filter feature to narrow down events
For this functionality you will need our Filter Bar extension which will allow you to set up different filters the way you like it. It looks like this on our demo site:

is there a widget option that would allow me to show 5 featured events
As per se Events cannot be set as featured or not featured. However, you could create a category called “Featured Event”. And then use the Event List widget, which will allow you to filter the events by category. Note, this requires the Events Calendar Pro plugin. See this screenshot:

Let me know if this answers all your questions or if you would like to know anything else.
Cheers,
Andras