Jet engine test facilities only really make sense when you have aircraft that can deliver backup engines on deck. One after the other, we will see the test facilities for jet engines - just not at 003.
No.several opinions about the 003 without engine test stand according to my knowledge: 1.003 is designed to defend and will be send to near mainland. that means it can go back to base to reload or repair the engine. 2.003 can carry several engine for the unexpected situation and do not need to repair and test them on the carrier.
China doesn't have a C-2 Greyhound equivalent.No.
Kittyhawk, Invincible, Clemenceau and Kiev class aircraft carriers were never limited to near-shore operations. So is Type 003.
With enough auxiliary logistic ships, a conventional steam powered aircraft carrier could be sent to and operated anywhere around the world.