Could I make a first person 2D game that looks 3D?

Yes, lot of old dungeon crawler games use 2D picture to simulate the FPS view for example (just look the gif on the main page of the event). So you can use 2D engine to make your dungeon crawler. Just keep in your mind that the only view authorised is the first person view.

Ok thank you

I might even say a "True" dungeon crawler should be 2D made to look like 3D... (this would disqualify my own game though, so let's not take me too seriously)