While I can't help you with Qt issues....
The kernel up until recently defaults to running in 32-bit mode, but 64-bit applications can still be used and run. This is why you have a 'no' for 64-bit kernel and extensions yet have 'intel (64-bit)' listed next to your applications.
My 2006 Mac Pro (Snow Leopard, 10.6.4) seems 'schizophrenic' about whether it is in 32- or 64-bit mode, and I think this may be the reason I'm experiencing a software disaster (below). According to the Mac website 64-bit is only supported starting in 2008. Under About This Mac -> Software, the entry for 64-bit kernel and extensions is 'no'. Similarly the output of
$ ioreg -l -p IODeviceTree | grep firmware-abi
| | "firmware-abi" = <"EFI32">
However, next to nearly every process in the Activity Monitor is 'Intel (64-bit)'. And when I installed Qt 4.7, it automatically installed the 64-bit version. It required that any library I linked to with my software (compiled under Qt) be a 64-bit build. I tried at one point to boot into 64-bit mode (not knowing that my platform wasn't among those supported for it) by holding down the 6 and 4 keys, following the advice here:
Anyway, installing Qt 4.7 (over 4.6) and doing this startup are the only things I have done to the machine, and now a program I wrote in Qt has stopped working. It has two processes and the main process can no longer communicate with the child process it launches (it doesn't receive standard output anymore). My guess is that this has to do with 32 vs. 64 bit sockets but I don't really know. Reinstalling 4.6 didn't help. Please please help, this program is supposed to run tomorrow!