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Re: Freestanding patio cover
1x lumber is 3/4"
2x is 1-1/2"
5/4 is 1-1/4"
It is called 5/4 as that is what you are getting, starts out different than 1x and 2x.
Those diagonal braces would be 'knee braces', and, yes, in most areas, you would want to install them with most construction methods. With enough steel brackets, angles, supports, etc., they would replace the need for knee braces as they would have a certain amount of built-in rigidity.
Nailed or bolted lumber does not make for tight and rigid joints. Meaning things can sway.
I would be careful about anchoring it to the house, you could cause leaks at the attachment points.
If it sways, regardless 'how much steel' is there, it needs bracing, typically that would be diagonal bracing or maybe just knee bracing (knee bracing does not extend down as far as diagonal bracing).
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