Yes you can sync your books to two separate devices although I am not aware of any compatible software for the Blackberry Playbook. You can find a list of compatible applications and devices at Digital Editions Supported Devices - http://blogs.adobe.com/digitalpublishing/supported-devices.
Also for information on how to sync your e-books please see Transfer eBook to eReader | Adobe Digital Editions - http://helpx.adobe.com/digital-editions/kb/transfer-ebook-ereader-digital-editions.html.
Finally you can download the software as many times as you would like. There will be only one installation of the application however.
As mentioned by Jeff, you can download to multiple devices from a single copy of ADE on a single computer. Whatever device is plugged in will show up. You need to make sure both devices and the computer are all registered to the same AdobeId.
Once the registration is complete, you will probably find you can also just copy the .epub files from your PC to a connected device using a file manager such as Windows Explorer. (You can copy them to the device without the registration, but won't then be able to read them on the device). Probably best to stick to using ADE in most cases (it should make sure annotations are copied properly and everything is kept clean), but file copy may be helpful:
- If you have a lot of books to copy.
- If you are using ADE 2.0, a Sony PRS-350, and the books are Overdrive library books. ADE 2.0 won't do the copying in this situation.