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Calendar and tasks sync between devices
(lemmy.ml)
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
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Nextcloud should be good for that. There are a bunch of services which offer a few GB for free, which should be enough for your needs.
I agree that Nextcloud is a great solution. Some other cardDAV and calDAV solutions exist, but Nextcloud provides much more. Here is a little demo of Nextcloud on a handset. https://videos.trom.tf/videos/watch/5fc16e0e-f95f-45a2-9843-37749bf9dada