I purchased download manager from Cydia years ago but it says that it's not compatible with my software (7.0.6) and doesn't work. Is there a download manager that works for the iPad air on this software?
If you download something in Safari there is usually a screen that asks where you want to open the downloaded file. If you have iFile, choose iFile and it will allow you to open the file you downloaded.
I'm using Safari Download Enabler on all of my devices. If you need more functionality have a look at Safari Downloader+ (which calls for $3.5, though).