Can anything cause the application server process to be killed by itself e.g., application code error. or this is only possible by manual intervention?
I can think of one instance. Memory. If WebLogic keep getting OutOfMemory exception for a while it can shutdown but not kill. You may have to analyze the log files to get more idea. Try running weblogic on verbose mode with GC enabled.
No the server log file. You can find this log in %WL_DOMAIN%\<domain_name>.log and in addition you can also check %WL_DOMAIN%\<server_name>\<server_name>.log