"At Regent, Monarch & Emperor, the AI can finally begin to do some meaningful research. Above that (I've heard), the problem becomes keeping up."
At least in the early game. Later on you can lead in tech.
To clarify this "Second, are you trading techs? At the lower levels, trading techs isn't very lucrative. As you move up, trading techs speeds up the tech pace and helps ensure that you've got a steady influx of cash." I think he means trading tech for gold per turn (gpt). Bamspeedy's "deity settlers" article in the war academy shows some examples of this on a deity level game in Vanilla
http://civfanatics.com/civ3/strategy/deity_settlers1.php. You won't get money like that unless you play the game on Deity or Sid level. But, I found it in a 5cc Regent game I played that you can get gpt for tech from the AIs at least after they have banking. On Emperor and possibly sometimes Monarch they only need to have had currency for a few turns... at least for the tech leaders. In a current Deity game I've played, I actually managed 7 or 8 gpt for literature from an AI before anyone knew currency.
"NO temples, cathedrals, colleseums, banks, stock exchanges, airports. Not all that many barracks or granaries. Courts in the 2nd band of cities, maybe 3rd."
Not necessarily. Temples and such can help you to work more tiles... thus more commerce towards science. Building at least 5 banks and 5 stock exchange enables you to build Wall Street which gives you more money. More money means you can research at a deficit, or you can buy more libraries/universities/courthouses/police stations.