how to understand the “thinking you ……not a place full of worry！”？
‘YOU! Look at you! Why, you are about the most ugliest thing I’ve ever seen. What an
embarrassment you are! Silly sausage, thinking you could pop your gross bunion head out of the sea and convince somebody of my princess-ish gorgeousness that the sea is not a place full of worry! I

YOU=Octopus

Question

how to understand the “thinking you ……not a place full of worry！”？
‘YOU! Look at you! Why, you are about the most ugliest thing I’ve ever seen. What an
embarrassment you are! Silly sausage, thinking you could pop your gross bunion head out of the sea and convince somebody of my princess-ish gorgeousness that the sea is not a place full of worry! I

YOU=Octopus

Answer

A lovely sentence, to say the least. x)

".., thinking you could pop your gross bunion head out of the sea ..."
Since she's talking about an octopus, she's saying the octopus' head looks gross (nasty), bunion = swelling. So the head looks like a swelling, basically.

"... and convince somebody of my princess-ish gorgeousness that the sea is not a place full of worry!"
The octopus told her(? or somebody else), that the sea is peaceful. Nothing to worry about! But the octopus looks so gross, there is no way somebody like HER would believe that.

"somebody of my princess-ish gorgeousness"
Somebody like her, who looks (almost) as beautiful (gorgeous) as a princess!