There is probably a whole bunch of different issues happening here.
Lion and ML have just as much problem with losing connection to the TC as the windows computer will.
I suggest you do a factory reset of the TC..
You then need to set it up as a straight SMB (windows networking) device.
All network names must be SMB compatible. Short, no spaces.. no apostrophe for sure. pure alphanumeric.
That includes TC name, wireless name/s, passwords of course. and even the hard disk name.
In the file sharing page I would also turn on the guest access and set the WORKGROUP. Although that is more for disk sharing they should also help print sharing.
The printer name, I am not sure.. but you want that as simple as possible as well and following the above rules.
I am not at all sure the latest firmware is the panacea to all ills.. in fact I tend to run any TC i have on 7.5.2 and find it works better. Especially the older ones.
If it still doesn't work, it is a case of buy a new network printer.. when this lot of toners finish.. buy a new printer instead .. make sure it is network capable. Far better than using usb printers and since printers are cheap cf the consumables.. well worth it.
Also make sure it is airprint capable and preferably postscript as well although I don't know if the combo is available.
It appears that HP has apparently not provided Apple with a specific printer driver for your CP1025.
See the list of supported printers:
You might want to check directly with HP to see if they have a driver that you could download and install that might work.
Is there any difference while plugging the printer directly to your Mac and not through the Time Capsule?
Connecting to your Mac is a "direct" connection.
Connecting to the Time Capsule is a "network" connection, which requires a "network" USB driver. Check with HP to see if they might have a "network" USB driver.