1. When large monsters move, they shrink down to just one square. So if a large monster that is two spaces away from a hero moves two spaces so that the monster is now adjacent to the hero (before setting its figure back on the map), then sets its figure on the map and attacks the hero it is adjacent to, can the large monster finish the rest of its movement starting from any space its base's new location covers (similar to how it first started its move before attacking the hero)?

2. If a monster double walks, can the monster shrink to one space, move its movement, unshrink (set figure on map any way you want), shrink down to one space again (gaining some effective movement depending on how large its base is), and move again?

45 minutes ago, The MechE said:

1. When large monsters move, they shrink down to just one square. So if a large monster that is two spaces away from a hero moves two spaces so that the monster is now adjacent to the hero (before setting its figure back on the map), then sets its figure on the map and attacks the hero it is adjacent to, can the large monster finish the rest of its movement starting from any space its base's new location covers (similar to how it first started its move before attacking the hero )?

All correct. A large monster expands when its movement is interrupted, and performing an attack counts as interrupting the movement.

45 minutes ago, The MechE said:

2. If a monster double walks, can the monster shrink to one space, move its movement, unshrink (set figure on map any way you want), shrink down to one space again (gaining some effective movement depending on how large its base is), and move again?

Yes, that's how large monster movement is designed to work, it's compensated by them typically having relatively low speeds.

Take a look at the pages 26/27 and 85 for examples of the CRRG at http://crrg.descent-community.org

Regarding your second question: You can't arbitrarily interrupt your movement.
You may only expand for a valid interruption reason.
Using your second action as movement is a valid interrupt reason.