What is the ruling on saying: "May Allah illuminate [you]" and responding to it with "And upon you likewise," and saying "illuminated/radiant" and responding to it with "This is your radiance"?

The phrases mentioned are permissible, and there is no objection to them. They are good words that include supplication, praise, and commendable courtesy. The default rule for verbal and practical customs is permissibility, as long as they are free from Sharia violations. Nothing is prohibited or disliked from them except what the Lawgiver has forbidden or what contains a Sharia-wise corruption. The Quran and Sunnah have indicated this.