1. You can still use that port, just insert the optical cable along with a toothpick or something similar to hold the cable in place. It's not usually the "door" that holds the cable, rather a "detent/high spot" inside the port, which may now be warn down, or simply inadequate (perhaps because of the missing door, but the toothpick or other thin object should compensate enough to hold the cable in place.
2. As mentioned in the bolded part of the DD5.1 FAQ which I provided to you earlier, some TVs require you to change certain settings in the audio menu to allow for DD5.1 signals for "passthrough" signals (from say HDMI). However, some TVs do not allow this at all and require you to connect the device directly to the AVR.
FAQ - What's Available in DD5.1
3. There are "optical splitters" that can be "reversed" to become "optical combiners" and in that way you can run two devices to one input, however, the devices need to be able to be turned off individually in order for the other device signal to get to the AVR. Most STBs do not "turn off" when they are turned off - they are simply in standby and there is still a signal on the optical port. You can usually tell by seeing the red light at the end of the optical cable. Most BD players, etc do turn off.
4. There are external optical switches (manual and with remote) that you can purchase to do the same thing - two (or more) inputs to one output.
If it works, the toothpick (or something else thin to hold in the cable) is the easiest.