I can't install the new update. I think it's because the version shows 0.3.2 rather than 0.4.0. Maybe this is similar to another app that I had to update in the past but only shows "lower version". Should I uninstall for a new one here?
Yes, you need to uninstall the old version before installing the new one. Updating via the APK installer does not always work correctly because the build is made for the old Android version to transfer saves between versions automatically.
EDIT: I also just tested updating from version 0.4 to the next version, 0.4.0.5, without deleting the old one, and it was successful. I think it's because the new versions are made differently and now include all the Acts together. Hopefully, with the next versions, there will be no more such problems.