Am I correct in understanding that all of the figures in a group stay on the board until the total health of the group is reached in damage, then the entire group is removed at once? Also, since groups have multiple models, can they move away from each other or do they have to stay within a certain distance of the other members of the group?

The health indicated on the deployment card applies to each figure in the group individually and the damage done needs to be tracked for each figure individually. As an example, for stormtroopers, each figure has health of 3 and when any single stormtrooper in the group suffers its 3rd damage it is removed from the board but the other stormtroopers in the group remain on the board until they each suffer their 3rd damage. When the last figure in the group is knocked out then the card is no longer available for activation until it is redeployed by paying the appropriate threat to cover the cost of deployment.

There are no restrictions requiring figures from a group to stay together.

Edited for grammar.

also there is a reinforcement cost on the card next to the larger number (stormtroopers cost 6 threat to deploy, and 2 threat to reinforce; bring back a figure that had been defeated.)

so that tells you that the figure when defeated is removed from the board