Karen, I'd be bothered by that gap too. If you do replace the steps, I'd extend them all the way to the side wall if possible.

If you don't replace the steps, maybe replace the existing brown lantern/pot(?) with something brighter, maybe a container planting on a pedestal, with an uplight beneath it so it's not a black hole at night? A tree with uplighting would be lovely, but I can't think of any species that would be narrow enough for the space and not so tall that it would obstruct your mailbox.

Bringing the steps all the way out to the garage would look positively massive… I think you probably don't want to do that. You also probably wouldn't want to create a puddle at the bottom of your steps.

You should be able to install a drain inlet beneath the downspout that could run beneath the walkway and out into the landscaping, with a "pop up" outlet at the end of the run. Talk with a licensed landscape contractor about that—they can determine where the best location would be for the outlet, and how to build the system.

A brick mason can build you a brick-facade box that will fill the space where the urn is now. It would be level with the porch and come out flush to the house wall, no need to move the railing. They can probably get a pretty good match to either the concrete porch color (after it is pressure washed it will be lighter) or the reddish bricks.