I understand that if I want to do the exact same action more than once, I need 2 samurai on the board (e.g. to build twice using 1 Authorization Card), but as long as I am doing it on different Authorization Cards, I can work my 1 Samurai to death?
You understand it correctly. Each Samurai can be used once per action, i.e. up to three times per round. Although you shouldn't work him to death...
I can move those 2 Samurai anywhere I want for free?
Yes, you can! So in total, a "move for free" action can save you up to 12 Ryo (6 Ryo per Samurai).
anyone can pay money to move the Merchant
But fortunately, you found it! And yes, you may move the merchant for money before ANY of your actions (like your Samurai), even if it will not be used in the coming action. But you may NOT move the Merchant with the aforementioned "move for free" action.