So thanks to
Outbound syslog messages truncated at 1024 bytes in size (broadcom.com) I found out my problem for point 2.
They are still truncated at around 10K characters even though i've setup the property to 1048576, but it is still much better.
Point 1 with hostname still outstanding, even with a reboot ... the system hostname is correct everywhere I've looked, but it seem the Gateway takes it from somewhere else... (reverse DNS lookup?)