How's data written to the database

I am trying to clarify the process of how does data gets written to the database. So far I can see the following:

Transaction starts
Required data is found in buffer chache or datafile
Data blocks are modified in buffer cache and are written to the log buffer
When transaction is committed, LGWR writes the dirty data from the log buffer to the redo log file
When checkpoint occurs, the data that was written to the redo log file gets written to the datafile

Is the above correct? Anything I am missing?

Also what happens to redo logs after the data from them has been written to datafiles?