I'm arriving at Dubai into Terminal 3 and the Europcar desk is in Terminal 1. Is the desk airside or landside (before or after immigration)? Can people pick the car up from Terminal 1 if they are arriving in Terminal 3?
If I understand the question correctly, you're asking if you can get to your rental car (located in terminal 1) from your arrival in terminal 3.
Getting between terminals is easy at the airport - I've done it many times. Their desk is absolutely outside of immigration, customs, and security at arrivals.
Simply go through all the bells and whistles, take the little metro between the two terminals (or the 24-hr shuttle if you want), and find Europcar in Terminal 1 at Arrivals. Happy travels!