How to get log file for rsync operation? Does rsync also delete remote files?

I am planning to use rsync for a daily backup to a remote backup server.

When I read the rsync manual it does not become clear on how to write a log file for the rsync operation.

I am missing options like:

rsync ..... -logfile=\home\backup\rsync.log -logmode=append ......

Did I miss these options?

I want to write (append !!) to the log file:

- Which files were transferred
- When the rsync operation took place
- How much bytes were transferred (total sum) in the rsync operation

How can I get such a log file otherwise?

BTW: Does rsync delete remote files (from previous rsync operations) if they are not existing
any more on the source system ?

Goran