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This is a pretty common design. 
Theres a CTA in the hero and nav with the same CTA and when you scroll to the bottom theres also another CTA that says the same thing. It feels a bit repetitive to me, but then again, I see it every where.
Are there any studies or research regarding the usability and conversion of this design? What are your thoughts on this?
It does depend a lot on what you offer , who your customers are and what value proposals you have in the sections and the truth might be in some A\B testing. I observed myself when I landed on a page, I scrolled down for a bit and was ready to sign up and scrolled a bit up and down looking for the CTa and it was just placed at the top causing a bit of frustration that could have been avoided by having CTA between sections.
You might find studies done on specific websites, but the result may vary a lot depending on the site. It's true that you can see repetitive CTA across many sites and this could be a bit overloaded. a good solution for this is to create contextual copys for the CTA, so even though you redirect the user to the same page, the message on the CTA will be different depending on where it's placed.
So you can find:
As Cristian said, A/B would be the best solution to find the right combination for your specific site.
