Yes, you need to download and install the apk each time.
Have not heard of a method of offering update patches for android that works properly and isn't a headache for the end user.
Your saves will remain as long as you don't uninstall the app.
You can backup your saves if you're using a file manager able to access this route [Android/data/com.domain.corruptedkingdoms/files/saves]
the persistent file and the files with the (.save) extension are important.
If the update fails, most of the time is that you don't have enough free space... Despite being a 1GB apk, android often asks for 2-4 times the size of it.