The original bug has been long fixed, it’s where clicking on the “Sync Now” button doesn’t actually work after a user has been offline for a while. This was originally due to an issue with the backoff mechanism implemented to prevent overwhelming the sync server in case there was an issue.
In your case, pressing the hamburger menu should show you whether your changes are “Saved” or “Synced”.
I feel syncing seems to be less frequent even the smart-phone is connecting to WiFi.
Hmm I’m not sure why that’s the case, but in theory it shouldn’t be. On every sync attempt, the app checks that the OS reports that you’re on cell network/data, and if so, skips the sync until a bit later. If you don’t mind the data usage then that shouldn’t matter.