It's a Phalaenopsis. It's what we call a splash-petal phal because of the markings that look like it has been splashed with paint. Normally I would say there's no chance of finding the name because there are so many hybrids many of which look similar but in this case splash petal phals are a fairly new breeding trend and you just might be able to find the name of this one.
Your potting plans are all good. Physan can be found at just about any retail outlet that carries a good selection of gardening supplies. Most chain nurseries, garden centers and DIY stores will carry it.
The great thing about physan is that you can mix it (according to directions) with the water you use to water your orchids so if you can't get it before you have to pot your phal you can still use it.
Regarding your 5th pic, you could probably cut the stem off below the last root if you're reasonably sure it is dead. Wait for a second opinion on this point.
I think you have reason to be optimistic. You've done a good job with the roots and it sounds like you're going about things in a way that will give you the best chance for success.
