This site, http://midwestfiberartstrails.org/listing/, the one you are trying to copy is using the cMap template. This is the template I would recommend for you. It supports the category drop down filter, the keyword search field and a Google Map “out of the box”. See the demo on this page of cMap.
Configuring cMap is the easiest because it utilizes the Customizer to provide you with a point and click interface and a live preview. It includes many options including support for how the image is scaled/cropped as well as many visual styling settings to control the color of various elements within the template.
The little map in the sidebar of http://midwestfiberartstrails.org/listing/ is not a feature in Connections or any of its addons. Looking at the page source of the site, it appears they are using and iFrame widget and ebedded this page, https://www.jimapco.com/maproom/midwestfiberartstrails/rsp.html, within the widget’s iFrame. The map appears to be created with this service: http://www.jimapco.com/.
Your last post mentioned this site: https://newsroom.findlay.edu/experts-guide/. It does indeed use the Excerpt Plus template which does include the category drop down filter and keyword search. It does not yet support displaying a map of the entry on a map. It also is more difficult to configure on because it requires configuration via many shortcode options vs using the Customizer. Also, in regards to the image, you would have to “preprocess” image before uploading them to the entry so they will scale and fit appropriately within the thumbnail size available in the template.
You have provided a lot of details. I hope I have not missed anything and have provided you with clear direction. Hope this helps!