If I have a creature equipped with Skyfall of Areion and Last Rites, do the effects trigger twice? Since Last Rites grants a Conquer AND a Hold ability, when I conquer do I trigger both, and when I hold do I also trigger both?

No — Last Rites is one triggered ability, not two, so it triggers once on a conquer and once on a hold.

"When I conquer or hold" is a single ability with a compound condition (Rule 383.1) — it doesn't split into a conquer trigger and a hold trigger. Skyfall of Areion's "My hold effects are also conquer effects, and vice versa" is a passive that reclassifies which category the ability belongs to; it never duplicates the ability. That matches FAQ #12659, where the same combination only fired once.

Both effect-text boxes do get appended to the equipped unit (Rule 136.2.c), so the unit legitimately has the Last Rites trigger and the Skyfall passive sitting side by side — they just don't multiply each other. What the reclassification does change is how it interacts with other cards: since Last Rites' ability now counts as both a conquer and a hold effect, a "your conquer effects trigger an additional time" or "your hold effects trigger an additional time" source will double it — but one such source gives one extra trigger, not two (and note it still fires only when the actual conquer or hold happens, not both for one event).