How can I transfer ALL my data (included a ton of memos) in my BB Q10 to an iPhone 5S?

If you're talking about Remember app, simply click "Share" on each intended entry to your email or Evernote account. Done.
In the long run, though, I highly suggest you use Evernote for all important note taking and memo making. Much less headache in the future. Guaranteed. Lol
The BlackBerry 10 OS is able to integrate an Evernote account into BlackBerry Remember. By doing so, entries added to the Evernote folder in Remember on the BlackBerry 10 smartphone will wirelessly synchronize the entries to the notebook in the Evernote account and adding entries into the Evernote folder via the Evernote account on another device (PC, Mac, smartphone) will synchronize the entries to the BlackBerry 10 smartphone.

Are the Notes saved locally or within an Exchange account?
If locally, then follow the above instructions and share them to a common platform (email).
If they're in Exchange then they'll sync via ActiveSync to the iPhone.

Only because I cannot load Viber on my Q10, I need to go to an iPhone 5S but need to know how to transfer ALL of my data from the Q10 to the 5S. Especially, a ton of info I have in a lot of memos. Thanks!The last time I checked, Viber works fine on BlackBerry 10? What's the problem you're having loading it on your Q10?
Posted via CB10