I am just the man to talk to. I go there 4-5 times a year to visit friends.
Places to visit, Casco Viejo(old part of the city) but very beautiful.
Gamboa, you can visit the rainforest
You can take a plane either to San Blas or Pearl Islands to visit amazing beaches. They are only about a 20-30 minute flight.
Common sayings, just say "Buenas"to greet anyone, doesn't matter he time of day.
Also if you want to get a womans attention at a store, preferrably one younger than you, say "Joven!"
The buses there are called "Diable Rojos" they cost 25 cents, they have new metro buses that cost a dollar and will take you anywhere.
If you need a taxi be prepared to pay the "beloved patriot" fee. It still is a deal regardless. Also if you take a taxi, never enter one that has another person in it. You will get robbed(but dont worry does not happen a lot, you are just as safe as any other city, just be street smart). Do not drive around yourself there, trust me, no one pays attention to any stops signs or anything there. They drive very crazy.
Brush up more on your Spanish, trust me, they say they are bi-lingual there, but I beg to differ, they may be able to speak some English but any local shop will look at you funny if you try to get something in English.
Dollar is the same there, the only difference, they use different coins both US and the "Balboa" also Balboa is a beer there, tastes alright, but not the best, you will find name brand beers much more expensive.
Note also, Panamanian Spanish, it is common no to use the "s" as much, por ejemplo "Como eta' " It can sound strange the first time you hear it.
I dont know what you look like, but if you are "white" don't worry there are a ton of Americans, Canadians, Europeans, living there. You will find many Black and Chinese there also because of there history, many people there mixed with a little bit of this and that.