My proposal is mainly based on the character of your house and especially is the shape of existing space.
the cover patio follow triangle shape will provide maximize space for seating area and match with the order of existing space.
I am also recommend traditional style for the patio and balcony to match with existing house and garage. And remove some ugly palm trees along the wall, just keep two large palm trees in the entrance drive way and rebuilt stonewall to enhance outdoor landscape.
Thank you for interesting project and hope you will find the best solution to your home.