Wow, what a gorgeous plant, great growing! Your lovely Phil looks like
Blushing Philodendron (Philodendron erubescens)
More information can be found here:
http://www.exoticrainforest.co...
In nature, P. erubescens climb trees and can grow as high as 50 feet or more ... and from the looks of your plant, if it had a tree to climb, it would be out the roof!
I agree with mj, with all those adventitious/aerial roots, you can propagate it by taking cuttings and potting them up separately, making sure you get as many of the wayward roots under the soil as possible.