Topic: logs

[Sander]

I looked at my logs just now and i found out that all the logs were duplicated and added the extension .1 like  
/var/log/messages and the other is
/var/log/messages.1
Is this normal?
I havent removed anything from the logs.
How often shoud i clean the logs(delete them)?
Is there somekind of a log that monitors that the other users dont do anything illeagal e.g. ping of death and so one. i dont want my ip address to be dirty.
is this possible?

Sander