How to work with Moth growing second stem

[HiOrcDen]

I have this Moth Orchid, which I believe is the correct term, for the ubiquitous Phalaenopsis with large white flowers and tiger striped center.

They arrived in spike, and by now all the flowers have withered. I haven't cut them off.

A second stem is growing really fast, and starting to spike.

Will the first stem regrow flowers, if I do nothing? Will it rebloom if I cut off the withered flowers at the stem? Will I have to use keiki paste to make it rebloom?

Or is the only the option to the original stem with wilted flowers, is to try and make keikis, and cut it apart to propagate it?

Ideally I would like to try and make a specimen with this one. So which of the methods I've mentioned should I use?

Will the first stem rebloom if I do nothing? Or do I have to cut the dead flowers off? Or do I have to use keiki paste to reflower?

Does the fact of the second stem spiking quickly, have any impact upon the method for the first stem, with the wilted flowers?