I think you need to head to the Photo section of Houzz and start browsing tropical gardens ans outdoor areas. Some beautiful photos there for inspiration. Then the helpful crew here in Design Dilemma can answer specific queries. Don't forget to save your fav photos to an ideas book.

I like a feature in each.

what can you see looking back at the house from the courtyard and the undercover area? what rooms overlook these areas? will the entertaining area be used by crowds or smaller groups? do you need to walk through these areas to the pool? what size pizza oven and barbq are you planning? what do you use the undercover area for now? what is the size of the undercover area? have you consider an outdoor kitchen in the undercover area with small table for everyday and a big dining table with market umbrella in the paved area and the fireplace with seating area at the far end of the courtyard

I know you said that you don’t want to paint the brick but between the ceiling, brick and paving there is just so much brown hard surface which will work against your goal of a cosy feeling. Do you need to keep it fully roofed? I’d suggest some outdoor rugs, in a lighter colour, to define the seating and eating areas. Timber or wicker furniture def no glass or metal. And a lot of plants and greenery. To get comments of layout you need to post a sketch of the floor plan of the space with measurements.