A ketubah is missing/destroyed (either Orthodox or non-Orthodox), the couple wants to have a new ketubah- what's the process? Should someone who was at the original wedding be an eid (if possible)? What's the status of the kids? Is it debatable for any reason? After the Holocaust, when presumably people were reunited did they redo their ketubot? (How was there proof for remarriage that a spouse died during the Holocaust allowing the other to remarry? What if the spouse surfaced later?)

AFAIK you get a new kesubah with a different type of wording. I'm not sure what you mean about the ortho/ non thing. Halachic judaism works a specific wa, according to your posek.

The whole agunah thing should really be a separate discussion. It is complicated, but when there is an agunah situation a rav can matter (allow) her to remarry. Hopefully he investigated thoroughly enough that the dead husband never shows up.

Re: the first part- perhaps a couple was originally married in a non-Orthodox ceremony, but now wanted an Orthodox ketubah.

What's the big issue, why can't you just write and sign a new one with 2 eidim present? The eidim on the Kesuba are often not the same as the eidim for kedushin anyway....

What makes you think any given non ortho ceremony is valid?

Not saying it is, necessarily. How/what would children and descendants of people non Ortho be considered?

What do you mean?
Whether the parents are married halachikly has no bearing on the status of the children. What makes you think it would? Kosher gittin matter very much though.