Can someone tell me what does the symbol mean in the formula for energy compared to amplitude? Looks like a partial infinity sign, almost like a fish symbol.
It seems that "fish" refers to $\propto$. It is means "proportional to". Since @Kyle Kanos has provided useful links about this, I won't repeat them.
But I want to add a useful tool for checking unfamilar symbols: http://detexify.kirelabs.org/classify.html
You can draw the symbol and get its latex code, and then it's easy to find its meaning (usually the latex command name itself is enough).