That is a solid budget subwoofer that should preform well for you. To get the most out of that you'll want to get a "Y" type subwoofer cable so you can populate both inputs. This will allow you to get the most volume out of this unit.
I would think that a 10" sub with 100 watts would do fine in a reasonable living space. Especially coming from a passive unit that is probably less than 8" and who knows how much power. The powered sub should make a big difference in your experience.
I'm sorry to say but you're not. You have a HTiB that looks like an AVR and separates but it's really just a HTiB setup. You can tell by the limited number of inputs, passive subwoofer and no video switching/inputs at all.
The one saving grace of the system is that is does seem to have a...
If I understand you correctly you're looking for more power for you subwoofer. Assuming that you are using the LFE/sub out on the AVR you're dealing with a powered subwoofer. The only way to get more power to that would be to replace the amp or just replace the entire unit with a new one...