equipment does not work:

Hi osodolot and welcome here.

Dunno about Mirage ship, but that stuff works on all my fighters ( Persephone , Saracen and Redemption ).
Yes every ship and equiptment is damaged by radiation - shouldn't it be like that !? (<- not a ? )

Radiation affects your hull, it's not blocked by shields, so shielding your ship up is useless.

The extra armor adds extra hull points, but does not make it invincible to radiation damage. So you can spend 10 minutes in a radiation field rather than 5 minutes without that armor class 10 upgrade. (just as an example in minutes).

Radiation penetrates anything.
As simple as that.