Thank You for posting the screenshots. Sorry to hear that you have run into an issue with your Brain.
"After some sudden shutdowns, my computer restarted and Personal Brain displays a message (message 1) asking for update the brain database to be able open it."
What were the sudden shutdowns caused by (OS related problems, hardware problems etc...)?
"The issue ocurred with two brains in few weeks!"
Was the sudden shutdown you experienced a few weeks ago caused by the same issue as that of your most recent shutdown?
"At the first time, my external disk became unrecognisable by Windows"
Sounds like something is going wrong with your external hard disk. I see that you have run checkdisk to find and repair files on your external hard disk. Running checkdisk may find and repair problems at a given point in time, but if there are problems with your external hard disk you may find yourself back at square one (attempting to repair your files etc..)
At this point, we would like you to try the following:
1. Close PB if open.
2. Create a backup of your Brain by making a copy of your .brain file and _brain folder.
3. Copy your Brain (.brain file and _brain folder) off your external hard disk into a folder on your local hard disk.
4. Open your _brain folder from your local hard disk then delete the folder "brain_db".
5. Re-open PB then open your Brain from your local hard disk.
The procedure detailed above forces PB to rebuild your Brain database from its backup, if the backup has not been affected from your sudden shutdowns, you may be able to get your Brain back open.
Please keep us informed with the results.