I have several different sponges growing in my tank. Most came in as hitchhickers. I have yellows, pinks, purples and white. Most are encrusting sponges. I have also kept the blue sponge as well. I've had both blue and the yellow sponges grow in both light and dark places in my tank. I do not feed the filter feeders in my tank directly but will on occasion add some filter feeder food to the water. Not on a regular basis.
As for their care, good wate flow is a must to get food to them. As for the air thing. I do a 50% water change on my tanks when I change water. My sponges and corals are exposed to the open air for about 1/2 hour during this time. That's including SPS and LPS corals. As long as you do not touch or bother the sponge, it will be fine. It's when you poke/prod at it out of the water that it may get an air bubble insid of it and die.
The blue sponges however seem more suscetible to being out of the water than others so I'd try to keep it in the wate during water changes. Another thing that I have found is that they are also susceptable to amoina spikes while other sponges are not. Don't ask how I found this one out.
With little effort on your part, they should grow just fine. I'm always finding new sponges growing in my tank where they weren't before all the time. It adds a nice little splash of color here and there. Good luck.