Since the Genius Bars at 2 locations were clueless about this and nobody here could answere, I thought I'd answer my own questions. After several more attempts at restoring, my 9 day old phone ended up slowly dying (rebooted itself, occassional blank screen and can't turn on/off, stopped charging, not recognized by my laptop, etc.).
I took it to the Apple Store and had it replaced. After my replacement, the restore went fine, without a hitch. So it looks like the backup itself was ok and it was a phone issue. Good luck to those who have this issue, I know the frustration.
This sequence solved my problem and the download started and is still going on:
1. Connect iPhone to iTunes and choose option of restoring to factory settings. Then iTunes start to download smth (800mb), restores my iPhone to factory settings.
2. After it is completed I disconnect the iPhone and did the procedure with selecting wi-fi network, and so on - as usual.
3. Choose the restore from iCloud and everything started to download correctly.
I am having the sam issue of lawst.
- settings were correctly restored
- camera roll has not been restored
- backup size (5.6 Gb) says that camera roll in included in the backup
Is now downloading all the apps, should have already downloaded the camera roll, or I should wait until it finishes to download the apps? My idea is that it should have downloaded camera roll already.