1. Gazebo: in this area I advise some changes in materials and colours that will emphasize the gazebo and sofas style.
I suggest to replace the stone paving with white deck and to plaster and paint white the brick walls.
The white colour helps to increase the brightness of this area and to exploit the sofas and gazebo style.
If you think that white wood needs too much maintenance you can choose glazed porcelain for exteriors that now performs extraordinary wood effect, both natural and warm.
As for TV I will place the screen on the wall, where now you have the hole that has to be closed when plastering.
Beneath the TV I will replace the kitchen with a sideboard made of white wood panels and light grey stone top; see picture in the furniture scheme.
The style is in harmony with the gazebo and you’ll have plenty of room for kitchenware, tablecloths and other useful stuffs.

2. Courtyard: in this area the sofas and lounge chairs are placed facing the garden and the house so you and your guests can enjoy a relaxing and beautiful view, at the same time the view of this seating area is particularly nice from your house as well.
The style of the sofas matches perfectly the ones you already have, the white colour is a nice variation on the theme and fits well with the bricks paving.
Behind the seating area I have placed the dining table that is extensible and to keep in harmony with the gazebo style and the bricks paving I suggest white metal; see pictures of all proposals in the furniture scheme, plus models and prices.

3. Kitchen: the idea is to create a kitchen island that doesn’t look like a kitchen but more like another entertainment area, like a bar island with some stools where to seat and enjoy the place not just for cooking.
To this purpose I advise three features: first a custom-made structure the same style as the one inside the gazebo, white wood panels and light grey stone top; see same picture in furniture scheme.
Second the side facing the dining/seating area will be a little higher to conceal the cooking surface; in the private resources you’ll find a detailed plan and measurements of the whole kitchen structure.
Third built-in outdoor kitchen appliances that help the concealment; I have found a charcoal grill designed to drop into the top of the island but I could not find a built-in oven specific for pizza, my advice is to opt for a built-in oven where you can bake your pizzas as well, but as you asked for a pizza oven in the furniture scheme I have suggested an outdoor model whose features look fitter fo the kitchen style than other models.
You didn’t ask for a refrigerator but, if eventually you think it useful, there is room enough to have it; in the private resources I have outlined this change in the kitchen layout.
To complete style and design of the kitchen area it is necessary to replace the stone paving with bricks, in this way you’ll have an even and harmonious outdoor area.

4. Vegetation: the plants that I propose are shrubs, perennials and one vine; see pictures in the furniture scheme.
They have a long flowering time and they are evergreen, this feature is interesting and nice in a warm climate like yours because you can always enjoy your garden.
Shrubs and vine grow big and high enough to create a natural fence, while at their feet smaller perennials add more movement to the garden design and prolong the flowering time.
Moreover the smaller perennials can be raised in pots to be placed in the gazebo and courtyard area as well; in the private resources you’ll find a detailed plan with the position of each plant and the quantities to buy.