Hi Ray, it looks like you may have a dendrobium hybrid involving species in section Dendrobium, aka 'nobile-type.' These generally like bright light, lots of water and fertilizer while growing, and a cooler, drier period in the winter.
The vegetative growths coming from upper nodes on the pseudobulb are known as keikis. Their occurrence often indicates the plant is stressed, though some species and hybrids in this section are more prone to them than others. You can remove and pot them up as soon as they have roots, but they'll grow better and bloom sooner if you leave them on the mother plant until they begin developing a second growth at their own base.
Your plant looks like it may be a bit overpotted, I'd suggest a quick repot to a much smaller container. These plants like tight pots with good aeration and drainage, otherwise they don't seem too picky about the medium. Mounting also works well if you don't mind watering a lot in the summer. Hope this helps!
--Nat