Very sorry for the difficulties, particularly any loss of projects (that is something that very seldom happens - if you have a backup of your iPad, you can restore it to get your projects back).
It looks like there are two separate issues here, the audio sync issues, and an issue with being unable to export a project archive.
For the project export, please close all apps (double-click home and swipe up on all screenshots), then restart your iPads, and try doing a project archive on a simple project with a single short video clip, and try selecting Airdrop/Other App. You should see "Writing Project", then you should see the 'share sheet' with Airdrop/Other apps. If it still gets stuck on writing project, then this is something we don't commonly see.
For the audio sync issues:
We've have recently found a bug in iOS that has to do with speed controls and can also be worsened by using "Maintain Audio Pitch". iMovie and other apps have the same problem. In our next version we are going to handle speed controls differently at the time of export in order to avoid the problem.
Here's the solution for now:
1. Make a copy of your sequence in the project manager
2. In the copy, go to any clip with a speed control under 2x, double tap on the clip and toggle Maintain Audio Pitch ON/OFF to make sure it is really off. Do this on just one clip on any track that has speed control clips on it.
Note: If you really want the Maintain Audio Pitch feature then put the source clip on a new timeline, set the speed and turn on Maintain Audio Pitch, then render that to the Photos app, then you can mark the in-point and use replace to put it back in your copy timeline.
3. Try to export and check if this fixes the problem
4. If not, then go through your timeline and look for clips with speeds over 2x and pre-render them out to the photos app using a separate timeline then put them back in your copy timeline using replace.
If you continue to experience problems, I would recommend you email us at firstname.lastname@example.org
. It will be easier to handle these issues separately and we can track them better there.