And yet they had to go back to Samsung for screens because no one else could really provide the quality & quantity that Samsung could.
Yeah; it's been a problem for them. Apple has been making strategic investments in these areas trying to create a healthier marketplace so they don't have to go to their biggest competitor to buy critical components. Fortunately, Samsung loves money more than it hates Apple.
LCD? Samsung used OLED for its top Galaxy devices since the day one. That was and is the main differentiator.
But you're right, being such a critical component of Apple's supply chain has likely given Samsung inside knowledge of Apple's platforms. As a result, Apple has been diversifying their supply chain to avoid Samsung.
I don't know that plays into their dominance of the Android market though. Samsung was already the top consumer electronics brand in the world prior to the release of the iPhone, so it's not surprising that would carry over into mobile phones. It was certainly a factor, though probably not a large one.