Two questions: can you link off of the focus action from an Ion Maneuver, or trigger other actions from any other card effects? Second, can you take any action if you have the Damaged Sensor Array crit?

The Focus action during the Perform Action Step of the Activation Phase is the only action you can do during the Preform Action Step , you cannot do a linked action from it or perform any other action during that step on the Ionized ship. You also cannot make use of any pilot or upgrade abilities that trigger on revealing or after revealing your dial since the Ionized maneuver replaces the dial and you do not reveal one.

That being said, the Ionized ship can be coordinated an action as long as it is outside of the Ionized ship's Perform Action step.

1. No, only focus. When Ionized, you are ONLY allowed to perform a focus action during your Perform Action step... so you can't link off of anything.
2. For Damaged Sensor Array , it's a little more complicated... but the short answer is, if you're ionized and have that crit, you can only perform the focus action during the perform action step.

As @Hiemfire said, you can always perform other actions outside of your perform action step, due to another ship using coordinate, or similar effects.

The explanations : Both Damaged Sensor Array and being Ionized limit your potential pool of actions in different ways:

1. Ionization says you can ONLY perform a focus action during your perform action step. It doesn't limit actions OUTSIDE of that step... just in that one window. A linked action would still take place in that same step... so it's still prohibited. If you can do an action outside of that step, you can do whatever you want. HOWEVER...
2. ...Damaged Sensor Array, instead, limits what actions you can perform at any time. You are only permitted to focus, or to perform actions on damage cards... nothing else. (This is particularly nasty against droid pilots, who don't have the ability to do focus actions on their own). Combined with the Ion effects, you're stuck with only the focus action alone (no fixing that Fuel Leak, sorry).