Will Dropbox delete a file from my cloud storage after I upload it?
So if I upload a photo with the Dropbox app, then delete it from the phone, will it remain in my Dropbox storage?
If you delete a file from your mobile device, the file remains on your Online storage.
To have the file permanently deleted, you need to delete it from your online Dropbox account, accessing it via their website.
I've just run this exercise (to prove the theory):
Dropbox doesn't work the same way on Android as it does on dektop platforms: It does not monitor a directory for changes. In fact, you only can download selected files, which will be saved on a cache directory on your Android device. The Dropbox app would not instantly notice if you delete the file. Only if you try do retrieve the file again from the cloud, the Dropbox app would search for the file in the local cache directroy first. If it isn't here, it will just download the file again.
But you can delete a file from the cloud storage by selecting the delete option in the Dropbox app. Same thing goes for upload: You have to select a file in order to upload it into the cloud.
As said before, Dropbox for Android works differently than the desktop program. It's just an interface to access your online account, with some special features like caching. For example, you can "favorite" a file for offline access and edit some files directly from the app. But if you want an app that works exactly like the desktop program, you can try Dropsync.