This is probably more general than 9900 specific but I am using 9930.

Using Blackberry Desktop Software vr: 6.1.0.35
When I perform a backup with the official desktop software, and with phone connected by USB. And with Full (device data and settings) selected
Are my installed applications part of what is backed up?

I ask because I had cause to restore from a backup to a new phone (of the same make and model), but many applications that were installed are gone.

Is that normal? If it is normal, is there no way to backup/restore everything?

Hello

This is fairly normal. Usually you can log into app world on your device and just simply re-install your applications. No repayments. Simple process.