Rambling directly on to here because the last time I tried organising it elsewhere it got derailed hard.
The little princess thing did happen, but it was at an age when he was too young to know better and he rather liked all the attention he was getting. He also got a lot of bribes so that people could dress him up so if he got something he wanted, he could stand to sit there and let people fawn over him for a while. It was only when he got older that he realised that he's not meant to be dressing up like that, but the damage had been done. That nickname follows him into adulthood.
The switch from Himewakako to the Demon of the Western Seas comes from his first battle. Historically he had his first battle late at the age of 22, but in SB I think it would have been a little bit earlier considering he is thought to be 22 in canon. The OVA had him surprised at Mori's douchebaggery suggesting that they hadn't had that many skirmishes. The unification of Shikoku probably happened about a year earlier at most than the events of season one of the anime. His first battle showed that he was quite the wild fighter and it was in that battle that resulted in the loss of his left eye. Even with that injury he continued to fight.
His eyepatch is wide because the scar is long. The circumstances surrounding it's loss was nothing like Date Masamune's where it was deliberately plucked out so there's a messy and jagged scar there. When he's by himself he doesn't bother with the eyepatch so there isn't a tan line. He's not ashamed of it, but he keeps it on around others in an attempt at showing off. There are stories passed around that he wears the eyepatch to keep his demonic eye hidden and he rather likes keeping up mysteries like that.
Being able to hold his own against Mori Motonari despite being the weaker strategist is most likely due to a combination of sheer luck and better equipment. He's an engineer and is constantly devising ways to improve their equipment and build better weaponry.
According to Matsu, Motochika has Iyo under his rule which is a divergence from game canon where Tsuruhime has Iyo and he has Tosa. I'll explain this away by saying she lives in her shrine there and tries to drum up a rebellion every so often against this annoying pirate who keeps filching stuff.