1. Broadband. By "Broadband, I assume you are refering to a cable modem, DSL, or satellite connection (ie: an Ethernet connection as opposed to a modem dial-up connection.) While there is no Ethernet port installed on the iOpener, you can use many of a number of USB Ethernet connectors.
2. Printers. That really depends on what the connection is and what are the driver requirements. This is very OS-specific, and don't forget that you only have one USB port. You could add a USB hub.
3. Sound. There are sound mods to tap directly into the sound channels, but it requires modding the "guts". Again, you may want to turn to USB. There are several USB sound systems available. These route and produce the sound through a device connected to the USB port. You would connect your powered speakers to this device.
In ALL cases, it all becomes dependent upon what OS you want to use:
I believe that the iOpener's OS is specific to modem dial-up connections (someone else may be able to elaborate.)
You could install Windows 98 and have access to just about any USB-based peripheral. There are known bugs or limitations with hight-throughput USB use, but there are also work-arounds and fixes. You will need to add a Harad Drive mod because Windows 98 will not fit in the SanDisk FLASH RAM. Just remember that the iOpener is a 200mhz machine, so Windows will work (some have gotten Windows XP to run) but it will not be that fast--very usable, but just not really speedy.
You can install a full distro after installing a Hard Disk mod or you can install a small distro into the SanDisk FLASH RAM. For that, I recommend "M4I" the Midori Linux distro for the iOpener. JailBait Linux is another option. Both of these small distros install in under 16MB, and do not require a Hard Disk to boot or run. They are not "complete" but they offer web browsing, MP3 listening, and a few other features.
That's about it.
I know I didn't give any specific links, but they can all be found here in this forum. Spend some time searching and reading. You will learn a lot and wyou will find your answers.
Good luck, and happy iOpening!