Does RMAN in Oracle only copy the archive logs? What happens to the active redo log in case of failure

No, you still need archived redo logs. An RMAN backup is not the same as a cold backup; when you restore it you need to apply all the redo generated from the time you started the backup until the time the backup completed in order to get the SCN consistent across all the datafiles and the controlfile.

Let us consider the old fashioned hot backup. In this mode, entire changed database blocks are written to the redo log stream, and the file is copied in the OS. This causes fractured blocks, i.e. the block has changed during the read by the backup. So to recover the database, we restore the DBFs, then the recovery process overlays the changed blocks from the archived redo logs onto the fractured blocks in the file, and we get back to a consistent database.

In an RMAN backup the problem of fractured blocks is eliminated because the blocks are read by Oracle via the SGA not by a Unix tool like cp. However the DBF changes between the time the first block is read and the last block, so it is the same problem, just at a larger scale. That is to say, the SCN changes between the first and last blocks in a backup. The archived redo logs cover this as well.

RMAN gives you the manageability of the catalog, and a means to do hot backups without needing to generate redo at a much higher rate (which puts its own stress on the disks, the backup system etc). However BACKUP DATABASE will not give you a consistent database in and of itself; the only way to do that in Oracle is the cold backup.

If logging with RMAN, you'd have to set the filename yourself - there's no wildcard. But there is an APPEND option.

spool log to 'my_log_file' append

Similarly, invoking RMAN with the APPEND option causes it to append to any log file specified.

Our backup scripts do the log maintenance at the OS level:

export LOGPREFIX=$ORACLE_ADMIN/$ORACLE_SID/rman/log/my_backup_script
export MYLOG=${LOGPREFIX}.$$   # add the pid to the log file name
rman log=${MYLOG} append <<EOF
... various RMAN commands
EOF

#Perform error checking and notification
fgrep -i RMAN- ${MYLOG}
if [ $? -eq 0 ]
then # we had a failure - email me
   mail -s "$0 : failure for `date +%m/%d/%y`" me@myself_and_i.com < ${MYLOG}
fi
# add the incremental log to the permanent log
cat ${MYLOG} >> ${LOGPREFIX}.log
# clean up the incremental log
/bin/rm -f ${MYLOG}