Some people say that the dollar symbol appeared when they started to place the U on top of the S. They put money from the US. Then it was merged to $. So at some point the dollar also could have had two lines.
In Portugal they already had a currency that was called Dinheiro in english money.
You're close. It actually came from the letters PS put together.
The peso was used in America in 1700s and the $ sign that evolved from peso was used in the US before the first dollar was printed.
I have a much better explanation of the bitcoin sign. Many currencies use their first letter like the euro uses a modified Greek E (Epsilon) so bitcoin used B. Many also have paralel lines going through the sign and it's usually explained as a sign of stability or equality.