Hi Candice
To remove your Basemap. You need to click on the burger icon in the upper left corner, then click On Device. Within the On Device screen you will see Maps and Basemaps. Click on Maps. You will see all your offline maps. For the map you want to remove the basemap from ,click the overflow menu (...) then click remove. You will have an option to remove the features or both features and basemap. Here you would would select feature and basemap. This would remove the basemap off your device.
Regarding the second part of your question on selecting another basemap. Do you want use the default basemap but define a new area for your existing map or do you want to download a new basemap to your device and use that with the same map?
-Carol