Root rot, terminal spike and a new keiki

[Jugyjoy]

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I am hoping that one of you good people out there will be able to help me with my new orchid. I have just purchased one white Soft Cloud Phalaenopsis (also called Willd [sic] Phalaenopsis Orchid) from an online vendor. They describe this variety as a regular, easy to keep Phal with lots more flowers than is normally the case.

The plant is stunning and I have fallen in love it, but unfortunately it came with some puzzling features, if not problems. I have questions about its leaves, stem, its flower spike and also a curious little shoot coming out from under the old leaf stack.

Stem
The orchid has lost one of its lower leaves and what remains is the sheaf rotting on the stem. On its outer surface there is a black smudge. To my naive eye the smudge looks like mould, and I might not be worried if it did not extend onto the adjacent root. Overall the affected area is rather small. (Please see the pictures attached).

Leaves:
Three (out of 5) leaves are turning brown from the tip. The discoloured areas are smooth and firm, but their colour is odd. I would perhaps know what this was if they were purple or at least purplish; but they are brown.


Terminal spike:
The plant has a flower spike growing straight out of its center. On an ordinary Phal this would be the so-called terminal spike and the orchid would be expected to die. Perhaps the Soft Cloud is different and this is quite normal.

New leaf:
A new leaf which does not seem to grow from the stem, but breaking through the bark it seems to come straight from the root. Is this a keiki?

Any help would be greatly appreciated.