Q: Do I need to back-up first before updating from 10.6.8?

You can upgrade without making a backup, but you will lose everything if the upgrade fails, so make a backup. Get an external drive and make a backup with Time Machine > http://support.apple.com/kb/HT1427

Also, note that OS X Mavericks is not compatible with all Snow Leopard apps, so first check that your applications are compatible > http://www.roaringapps.com Remove the apps which are not supported, or update them to the most recent version.

Finally, open the Mac App Store and download OS X Mavericks. The installer will appear when the download finishes.

1) Yes, do the backup.  You may want to go back, and you may need to restart if the upgrade fails.

2) Do nor publish system erial numbers or personal email or personal phoen numbers or ... I will ask moderators to edit your post.

You really should have 2 separate backups because hard drives fail. If you plan to backup using Time Machine, it will backup to 2 drives, alternating between them. Another option is to use a clone.

Clone  - Carbon Copy Cloner          (Often recommended as it has more features than some others)

Clone – Data Backup

Clone – Deja Vu

Clone  - SuperDuper

Clone - Synk

Clone Software – 6 Applications Tested

Commonly Used Backup Methods