Where I think you will need another I beam is where those front columns are right now. You can leave the column on the far right end, but you will need the beam to go from there to the gable end of the house. That looks like too long a span for a wood beam. even an LVL would have to be about 20" wide so that would hang down a lot. You might even have to open up the wall where the beam would tie in to put a steel post from the beam to a new footing at the ground level. There will probably be a lot of weight.
It might be possible though to get away with a lighter beam if the ceiling joists are fully cantilevered. I can't tell from the pictures. But anyway those existing columns would just get in the way of a porch extension.
I guess I can't appreciate just how narrow the porch is. It looked to me like it might be 3 to 4' deep. Four feet would be sufficient I would think, three is a bit narrow. How about this, leave the roof alone, frame in the arches like you are planning on, and the area below the porch, but put in one or two bow (bay, arched) balcony's with a curved wrought iron railing, kind of like you see in the old Spanish architecture. You could put a small wrought iron (looking) cafe set on each one.
BTW, you are wrong about that circle garden, it is beautiful, but then I like landscaping to look as native and natural as possible. There are no weeds, just bio-diversity.
If you don't need that driveway to circle, and it appears that you have a parking area off to the right side of the house in your first picture, then I really would consider getting rid of it and putting in a patio.