a+noun+ of OR the+noun+of (Which article to use)

Choosing the definite or indefinite article is often tricky, as it seems you have found. This is complicated further by the existence of many fixed phrases in the form of "a/the [noun] of [noun]" that break the typical rules.

In your examples,

1. Both would be correct, but there is a subtle difference in their meanings. In 1a, "a resumption" indicates that there have been other flight stoppages before, and that this resumption will be one of many through the history of the airport. 1b refers specifically to this particular resumption, and does not indicate whether there have been or will be other resumptions. 1a sounds slightly more natural to me (native American English).

2. "Under threat of death" (no article) is a fixed phrase and would sound most natural. Of your options, "under the threat of death" is more appropriate than 2b - one's life is either threatened or not (even if by multiple threats).

3. Again here we have a fixed phrase, "pose a threat". Neither 3a nor 3b sounds particularly natural because the fixed phrase "pose a threat" is colliding with the fixed phrase "[under] threat of death" (no article). You might instead use "pose a deadly threat".