In the first story, "to round out the package" means to make the story more complete, or to make the story more balanced. In (American) English, this is a fairly uncommon phrase, but you might hear someone say, "to round things out" or "to round out the set" to mean the same thing, 'to make complete.'
The sentences from your second link are mostly nonsense, probably said for comedic effect. The terms are nautircal (words related to sailing boats), but in this video they are changed so that they no longer make any actual sense. I defined what I could:
"Swab down the planks" means to mop/wash the decks of the ship.
"Hoist the main sail" (rather than 'moist the main snail') is also a nautical term that means to raise the large center sail to pick up more wind and increase speed.
"Keel" and "port" are also nautical terms. "Keel" is the movement of the ship on the sea. "Port" is the side of the ship. "Blubber" is the term for the thick layer of fat that whales and marine mammals like seals accumulate to keep them warm in cold ocean waters. "Keel the port blubber" doesn't actually mean anything as a phrase. Like I said above, it was probably just meant to be funny.