Percona XtraDB Cluster and MySQL Replication
it seems the binlog doesn't include the new inserts


I'm not sure whether you're saying the binlog actually doesn't include them, and you have confirmed this with mysqlbinlog, or that it "seems" like it doesn't, because they don't replicate.

PXC needs log_slave_updates turned on at the node serving as master to the asynchronous slave, otherwise, not everything will be written to the master's binary log.  This is very different than an ordinary MySQL server as master, where log_slave_updates will do nothing at all (unless the master is actually a slave to another master).

If that's not it, remove replicate_do_db and binlog_do_db and all of their related options from your configuration and then remove them from your brain.  They should never be added unless you know exactly how they work, in your sleep.  The simplest and by far most reliable replication configuration is, and will always be, replicate everything, which is the default.

Forget about binlog_format on the slave.  It makes absolutely no difference unless the slave, itself, has other, subtended slaves... and if the master is using ROW format, the slave will still log in ROW format if you do indeed have it configured with subtended slaves.  Also, the slave's binlogs (not to be confused with the relay logs) will not log statements received from an upstream master unless log_slave_updates is enabled on the slave.  

The same thing goes for innodb_flush_log_at_trx_commit.  It does not impact actual replication.  It's a setting the determines a tradeoff between ACID compliance and performance.