Does HADR copy the logs from primary to standby or does it transfer the log records using some memory area and then recreates them on standby? What happens to the logs on standby after they've been applied?

Log pages are transferred through network from the primary and are first written to the logbuffer on the standby and then written to the log file.

To add to the above remark:

If you use HADR Nearsynch mode, then the transaction will be considered as committed (assuming a commit is issued or auto-commit) on the primary when the log record is transferred to the HADR log buffer on the standby.

If using HADR Synch mode, the transaction will be considered as committed (assuming a commit is issued or auto-commit) on the primary only when the log record is written from the HADR buffer on the standby to the log file on disk on the standby.