Hi,
Just to be clear.
The app is Messages once you get to Mountain Lion or above and one of the accounts it can do is iMessages.
(The app on the iPhone is also called Messages and can send and Received iMessages as well as SMS).
That said on a LAN with iChat and Messages capable machines Bonjour is the way to go.
That said an iMessages account in Messages cannot connect to a Bonjour account in iChat.
I have a Leopard (iChat 4) and a Snow Leopard (iChat 5) and a Mavericks (Messages 8) computer.
Bonjour as text chats works between all of them.
I do have however, an issue myself sending files to and from the Messages 8 and iChat 5 computers and nothing I have tried has resolved this.
I do not have another OS X 10.9 machine to compare Messages 8 to Messages 8 with.
Idle is Messages and iChat is a specific thing.
It is the time after the last Keyboard or Mouse input which then changes the Status from Available to Idle (it also changes the Away to Away-Idle as well but iChat and Messages do not display this).
Nominally the Status change is at the 10 minute mark.
This is separate from any Energy Saving settings in the System Preferences or the times set for a Screen Saver to kick in which can be different again.
Could you go into more detail about what you actually mean by idle ?
7:43 pm Friday; May 23, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad