You have a Keiki (baby Plant) you should leave it attached to the flowering stem till it grows some new roots.
Not strange, some orchids readily make keikis.

Here is a link that might be useful: FAQ on Keiki

The keiki has never produced roots and is separating itself from the stem. See dying stem above the leaf growth. Can the new leaves be potted without roots? Or, what is your advice, please?

This is a very rare occurance and in time it will grow roots.
You should just leave it as it is for a couple of years.

You can cut it off if you think its going to fail. Apply some root hormone and place in spagnam moss and you may get another plant. Roots should form on the plant though