Goldfish need a well oxygenated and over-filtered tank yes. A bubbler is just decorative, it's surface movement you need, best achieved with a large established filter and a spray bar. Goldfish should NEVER be kept in unfiltered tanks.

I would, they need lots of oxygen in the water, but well oxygenated water also stays at a lower temp, which for goldfish is good. It doesn't really even need to be speced for the same size tank as long as the bar or stones, whatever you plan to use just keep it flowing properly.

No but you'll definitely need a filter.

yes !!!!!!!!!! !!!!!!!!!!!!!!