For the most part IMO sponges are another thing that just happen in a reef. Most times you don't buy them or add them deliberately they just happen. I would guess I have 10-20 different types of sponges in my reefs and only one of them I purchased. The first picture is of a blue sponge. In fact there was a time where having sponge growth was considered an indicator that your system was stable and mature. More recently people have come to think of them as annoyances or even pests. Then of course you have people that will scrape them off their rocks only to purchase identical ones later.. Jake Adams is one person who is always talking about how you should remove them. They can and will overgrow corals. One coral I neglected was an elegance that had a black sponge eventually almost completely grow over it. By the time I got around to removing it, it was too late.
Having sponges in your system would show that they can survive and or thrive in your system. Most of the time in my personal experience they are slow growing. They also don't have an issue being out of the water. I have another piece of that blue sponge that was out of the water maybe 20-30 minutes last week when I was fixing a rock that fell over. I actually recall buying it maybe 6 or 7 years ago asking the guy at the store to be careful and he told me that they are fine exposed to water. Not really sure where this idea started but I have been hearing it for years. Likely there are some species of sponge that cannot be exposed to water but for the most part that is not true.
Some are photosynthetic or at least partially photosynthetic where as some are not. In my overflow / sump and other areas that get very little ambient light sponges grow. While I have never personally tried target feeding them
@Dr. Dendrostein is probably a good person to ask about this. Their diet may be similar to some NPS corals with very small mouths.
The only sponge I've ever really had trouble with are those red and white aussie sponges with the gorgonian growing on them. Of course it's been many many years since I tried keeping those, so perhaps they would do okay now. You don't really see them for sale much anymore but when Australia was new giant colonies were constantly coming in. They are still available from time to time.
The first couple pictures are in my display (lights off) the rest are from my frag tank sump.