I don’t understand what this means: ”the grass would in front of the house be replaced and fencing upgraded for a swinging gate.” Does this mean you are widening the concrete driveway?

Also, I guess picture #2 is the backside of this same area as picture #1?

I'd suggest an UNattached carport to avoid the requirements and permits required to attach it to the house. This would would mean not a single piece of lumber or screw would connect to the house and would not be considered an addition to the existing structure that would not increase your property taxes.

Start with zoning. Distance to property lines of a structure (attached or accessory). Distance for impervious surface. HOA if you have one.

But no, the carport roof cannot match the slope of existing roof all the up to cover the carport. There is a window there on the 2nd floor and the carport roof would extend to the upper roof if it continued at the same pitch.

Your house design, level of value, and neighborhood looks like it wouldn't be a good candidate where a carport would fit in to begin with.