I like your ideas. You'll likely need a railing though. A simple white picket railing would be in keeping with your home's style.

If covering the whole porch, you'll likely need to remove the existing porch cover and rebuild it up higher to maintain a slope. If you don't need a fully covered space, an open pergola type extension cover could provide shade and cost you less money. Or install a retractable fabric awning shade.

Soften the concrete base with a boxwood hedge.

Add a dining table and/or some lounge seating. Loads of potential here.

Nice space you have there. I would start with your idea of extending the roof to cover the whole porch with white posts. Then add white railings around the perimeter. And to keep costs down I would just paint the concrete with a durable outdoor paint - white or the same colour as your siding to make it blend in. I could see this space being used a lot once covered. Good luck.

I would build a high screen wall of solid wood at the right side. This would cut down on the sound of the HVAC unit and make the area more private from your neighbor. Add a matching wood rail across the back and down the existing steps. Finish up with a table and chairs with a round removable canopy. I like the idea that anitanazar had for the concrete.