What is the origin of the saying "Hand over Fist"?
It means we're making money, lots of it and quickly.
The term has a nautical history.
It meant climbing a rope by hand on board a sailing ship. As you reach up, your hand closes over your fist below it.
The term hand over fist evolved from making progress up a rope to making progress generally, and then only to making money.

"Mind your Ps and Qs" means to mind your manners, mind your language, or be on your best behavior.
It may have come from English pubs and taverns of the 17th century.
Bartenders would keep a watch on how much their patrons were drinking, keeping an eye on their pints and quarts.

Why do we say someone is under the weather when that person is sick?
Again, we go back to the sea for this. Any sailor who was feeling ill would be sent below deck to protect him from the weather. 
Being below deck, the sailor would literally be under the weather.

We know what a couch potato is someone who  vegetates idly on the couch or an easy chair.
We know exactly where and when this expression was born.
Tom Lacino said it on the phone on July 15, 1976, asking about his friend, Bob Amstrong, a cartoonist, asking "Is the couch potato there?"
Armstrong liked it and actually trademarked the phrase in 1979. 
The Los Angeles Times used the expression on Friday, December 28, 1979  describing a float in the Doo Dah parade. Lacino and Armstrong dressed as potatoes on a couch watching TV. 
But Armstrong lost the trademark, so many people began using it.

"That's a horse of a different color!"
That's from Shakespeare's Twelfth Night, Act 2, scene 3: The character Maria says, "My purpose is, indeed, a horse of that colour..." meaning something similar. That's how we used it until around the mid 19th century, then it became "another color," meaning something completely different.