Using dropbox as database
Is it possible to build app whit integrated dropbox acc, and use this account for all clients? I want to upload images to dropbox, and all client apps can download it, or upload to this acc from my app? I have read all dropbox sdk tutorial from there site, but steal not sure if this is possible.
Not really. DropBox uses OAuth for authorization to allow users to login with their own accounts. Even assuming you figured out how to log in on their behalf with your own credentials you would be handing out your credentials to anyone who wants them, allowing someone to change the password on the account, etc.
Alternatively I suppose you could generate tokens and hand those out instead, however you'd have to setup some sort of web service for this, and you'd still have problems with people being able to do stuff to your account that no doubt you don't want them to do. E.g. I could create an app that just instantly deletes everything that anyone uploads, or I could create an app that fills up your quota with files filled with zeroes.
This is not what DropBox intends you to use the API for (and in fact it may be against the ToS, you should probably read to make sure if you're going down this route despite my discouragement). You should use a more appropriate storage method.