A few years since Ive been through CMB but comments from memory.
No arrivals lounge that I remember (although the terminal map shows something past immigration) - the terminal is single level so departing and incoming passengers mix.
I would guess three hours.
When I went through on a UL-CX 5-hr connection (before UL joined oneworld) I had bags tagged through and just went to coffee shop for a few hrs then transfer desk where a staffer took my passport down to the checkin desk (wasn't overly happy about it but didnt have a choice) -- actually that might have been KRT.