1) I understand that I need iCloud. Must I install it on my office computer? Is there away I can change the sync from my office computer to my personal laptop without loosing any data?
No, you understand incorrectly. iCloud is completely optional. There is no need to install anything on any computer to make iCloud work. iCloud is also unrelated to which computer the device syncs with.
2) Please confirm that I can back up my text messages, what's app conversations and contacts.
They are a part of every backup of the device done either via iTunes or iCloud.
3) After I purchase a new phone, how do I retrieve the data I saved on the iCloud to my new phone.
Restore the device from backup.
4) How do I erase all the data (e-mail accounts and everything else) from my old old phone so the next employee will not see all my personal history.
Restore it as new.
Thank you so much for the reply.
But the plot thickens...
I read that for iCloud I need to have an update ios version and of course I don't nor to I have the option to update without iTunes cause I have a really old version without the "software setup" icon.
Since I can't at the moment access my iTunes account at work ( I am on leave) what can I do?
Can and how do I change that my personal laptop that I have with me will become the computer that my iPhone syncs with?
Will I loose data?
After I figure this out I will continue with the rest.
Thanks again so much, you are a great help.
Okay, so the device is obviously running something prior to iOS5.
The options are backup to the computer the device normally syncs with and then restore the new iPhone on that same computer or update the current device on that computer to a current iOS version.
If you try to sync with a computer other than the one the device normally syncs with, you WILL lose data.