Hi FLO, that leaf/root thing could be a keiki, a baby plant. especially if it is growing out of the bloom stalk. It looks quite big and with strong roots, so I guess it can be cut off to be planted on it's own (experts please verify). This orchid looks like the Phalaenopsis type. Over here in Singapore, we either grow them in a pot of sphagnum moss or mount it on a slab of fern bark. Just don't keep it overly moist or the roots will rot. They like bright light but direct sun or too intense light will often burn the leaves.
Hope this helps.
Wish I could help with the orchids but I don't have any experience in that field. From the pic..it looks happy and healthy. Is that peppers I see on the right side? I've thought about trying a bush or 2 inside during the winter but haven't made the effort yet..
Now that you can see the pot it is in, is it big enough?
Should I discard the old plant once I re-plant the keiki?
That helps a lot. Thank you. I'll put up some pictures of it when I am done.