Anytime wood is refinished it should start with chemically stripping the finish off. Sanding the finish off tends to remove what is on the surface and leaves what is penetrated into the wood. Then when you go back with stain there will be spots that won't accept the stain because the wood is still sealed with the old finish.
There are types of wood such as alder, pine, maple and many more that have hard and soft places in the wood and a pre-stain conditioner is used to make those types wood stain more uniform. Mahogany isn't one of them. All a conditioner will do is make it more difficult to stain and make the adhesion of the finish somewhat worse.
A spar varnish is the right finish for exterior wood and there are two basic types which are a plain spar varnish such as the helmsman which are alright for applications were the wood isn't exposed to direct weather. If your door is under a porch where it gets almost no sun then it may work for you. If it is exposed to direct sun and rain then a marine grade spar varnish would be a better choice. A medium grade marine grade spar would be Cabot spar varnish. The best is Epifanes. It's formulated to use on the deck of a boat.
A gel stain isn't a very good stain for real wood. It was developed to be used on a textured fiberglass door to make it look more like real wood. It's like you mixed a brown paint and a varnish together. It covers the wood somewhat like paint but is transparent enough to see the wood. You would be taking a mahogany door and make it look like it's something synthetic.