When using Photosynth's mobile panorama app, it creates two differently formatted panoramas:
1) a cube map for interactive viewing and upload to your account here on Photosynth.net
2) a flattened panorama for saving to your device's camera roll, sharing a flat version to Facebook and Twitter, etc.
I'm assuming you're using an iOS device instead of a Windows Phone.
I don't have an iOS device handy so can't tell you what the default behavior is these days, but I think that as long as you allow Photosynth's app permission in your iOS app settings, Photosynth's mobile pano app will save the flat panorama to your camera roll by default.
If not, yes, you'll have to download them one by one by sharing them to email, Facebook, Twitter as a non-interactive pano, etc.
On Windows Phone you can also share directly to camera roll. I'm not sure if that option is still in the iOS version.
Yes, definitely upload each of your panos to your account.