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Let me take a look at your drawing.
Can I get back with you later this evening when I get home from the office?
Before we get started I’d like to point out that a Professional Engineer’s standard of care typically includes a site visit to assess field conditions and get an overall understanding of the structure. This can obviously not be accomplished through the internet. The information provided here is meant for planning purposes only (general sizing and budgeting) and is based on the information provided by you. All loading cases considered are for vertical loads only, no lateral analysis has been completed. The information should be verified by a professional engineer who can visit the site to ensure that potentially important information has not been overlooked or omitted.
You really need to cut an 18" square hole in your concrete slab, for each of your 6"x6" posts and dig down at least 36" and then set you pressure treated posts in the the holes and wrap the posts with 15 lb felt paper and pour the holes full of concrete. You need to drill two holes perpendicular to each other (the 1st one 6" up from the bottom and the 2nd one 12" up from the bottom) and place 16" long steel rebar through each hole before you pour your concrete. This will help with uplift resistance and also lock your 6x6 posts into your concrete and brick masses.
You still need to build your cinder block and concrete pilasters around your posts up to 32" or 36" above the patio slab. You need to also wrap roofing felt around any part of the posts that will be in long term contact with concrete.
You will need to have a local engineer detail all of your connections to resist the loads you’re your 6’ cantilevers in your roof system.
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So instead of approx. 6' off of one side, do you propose approx. equal 3' to 4' cantilevers off of each side of the center posts?
Even with this revised configuration, you would need some embedment into the ground with your posts