Without a photo, it is hard to be certain, but I suspect that those balls are some sort of slow release fertilizer. But that is only a guess.
If you want to repot this orchid, you can do it with the blooms on it, but take care to not disturb the roots too much. I personally would not divide the orchid unless you think it is too big for you to care for it. The more mature the plant becomes, the more blooms at the same time you will get. With two new growths, you can probably (with proper care) expect to see both of those in bloom at or around the same time.
I agree about getting it out of the sphagnum. That stuff is death for my orchids the way I water. Best of luck with it.