In an engagement is it forced to resolve each combat icon from a unit or can you just resolve one without doing the others? Like can you just do the tactics and tap someone and not resolve damaging someone with the unit damage icons?

Nope, see the rulebook on Resolving a Strike. You have to resolve any and ALL icons in groups if it is Blast or Unit and individually (but at the same time) with any and all tactics icons.

You can't NOT use them all.

What if you choose not to deal damage to a unit because of the reactions of a card ie chewbaca? It's more effecient to tap rather than release his rage.

What if the person forgets and doesn't fulfill all the icons before saying his strike is over?

The rule book does not say that the resolution of icons is "forced" only that it continues until all units are exhausted. If a person has completed their attack and not used all the icons and the next person begins there strike the unit is already exhausted and can't use it's icons unless it is "forced"

Pg 20:

To resolve a strike, a player follows these steps in order.
1. He chooses one of his participating ready units.
2. He focuses the unit to strike (i.e. places a focus
token on the card).
3. He resolves the striking unit’s combat icons by type.

You have to do step 3 to resolve a strike, and you cannot move on to the next strike until you have fully resolved the first strike (pg 20, a little higher up: "Each strike is fully resolved before the next strike may begin.").

You cannot ignore an icon type, when you resolve a strike all of the combat icon types that card has will be resolved.

If a person has completed their attack and not used all the icons and the next person begins there strike the unit is already exhausted and can't use it's icons unless it is "forced"

This is a "what if" that is not allowed by the rules. The person has not completed their strike if they haven't used all of the icons and the opponent is not allowed to begin their strike at that point.