Can a steel exterior door be gel stained to appear like wood ?

Yes. There are kits available that will give instructions on how to do this. The kit will come with the correct stain, as well as a wood-graining tool that gives the appearance of wood grain on a flat surface.

https://www.hunker.com/13411615/how-to-paint-or-stain-a-steel-door-to-make-it-look-like-wood

Yes you can use gel stain for graining.. You can buy individual graining tools. No need to buy a kit. I have made my own graining tools out of stiff cardboard. Just cut out grooves of different sizes into the cardboard end. Throw them away when through. Cheap but effective.

No, I would use a metal paint like Rustoleum, do the lighter color first coat, then when dry apply the darker color mixed with glaze and run a graining tool over it. Top coat with Spar Varnish.... https://www.youtube.com/watch?v=cwab2Eicqs0

Here is one using a stain, never seen this product..... https://www.youtube.com/watch?v=liQuCa1pyWA&t=60s

using the wood graining tool.... https://www.youtube.com/watch?v=MwROpn4I3pU