Totibbs
Trading is very much subjective - what is fair value depends on lots of factors (ie tech is worth more if only one civ has it). The AI will usually offer just below market value if you use "what may I get for world map". You can normally add 10 or 15% onto the price he offers. (eg if he offers 200g, try for 220g or 230g - it's unlikely he would pay 500g for it).
No, You shouldn't build every building, but here are some basic guidelines to work with.
Walls (You can build these in every city if you want to (no upkeep cost), but don't bother in fast growing cities by a river)
Barracks (Build in your unit production cities, or on an enemy front. Don't build barracks in your economic cities)
Temple (build if you need happiness / culture)
Library (build if you need culture, Or if city produces 2+ science)
Marketplace (build if city produces 2+ gold OR if you have 3+ lux and need happiness)
Aqueduct (only build if pop is 5 or 6 and city has plenty of extra food)
Harbour (Build for trade routes, veteran boats, or if city needs extra food from water squares)
Colusseum (Best to wait for cathedrals if you can - only build if you already have cathedral)
Cathedral (build in large cities that need happiness / culture)
University (Build if city produces 6+ science OR for culture)
Coastal Fortress (build if you have nothing else to build - they are almost useless, but cost nothing to maintain)
Bank (build if city produces 6+ gold)
Factory (people will have different advice on this - I won't build a factory unless it can be built in less than 20 turns)
Power Plant (Most cities that can use a factory can use a power plant)
These are minimums, or break-even points. I won't usually bother with a university unless the city is producing 20 science, not 6. But the above numbers should prevent you from going backwards by building an improvement.
By the time you reach the modern age, you may well have every building in every city. But in the Ancient era, you can't afford to build stuff that is going to add cost with no benefit. Try to figure out if you need a particular building, and if you don't then consider building more units instead. If you already have too many units, consider "liberating" your nearest neighbour.
Edit: oops, forgot about the courthouse in my list. I myself are often stuck wondering if I should build this or not, there is a lot to it and it also depends on government (ie a city that needs a courthouse in despotism may not need one in republic). Here's a beginners rule of thumb to get started with:
Courthouse (build if city has 7+ wasted gold/science but is otherwise productive.)