A few comments:
1) Thebes: I can hear Dave screaming already. That city with all the riverside grassland sounds like a cottaged capital, perfect for running Bureaucracy. Two bonus food resources is great for any city, but for the uber-GP farm you really want 4-5 food bonus tiles. A captured AI capital is often perfect for this.
2) Importance of GP farm: Having more specialists is handy, and you usually can get similar performance to cottages during the early-mid game if you have enough specialists going, particularly if you're running Caste System. Specialists give you a lot of flexibility. That said, I have played many games without a food-driven GP farm, and you can generate specialists with multiple mini-SE cities running a couple of specialists each, or with a wonderspamming city.
3) GP Farm better in SE or GE? Arguably it's better in a CE, because most/all of your GPPs are coming from one place -- the GP farm isn't competing with other cities for specialist generation, which becomes an issue when each GP starts costing over 1000 GPPs. That said, a CE thrives in a different set of civics from a SE, and the GP Farm will be better and more flexible in Representation and Caste System. The GP farm works well with either.
4) prioritization of GP farm in CE: If a GP farm candidate presents itself, then yes, it is a priority. The main requirement for a GP farm is a lot of food and either Caste System or a ton of specialist-enabling buildings. Since many GP farms are captured capitals, it's usually easier to get the specialists going with Caste System, which you may or may not want to run with a CE.
5) Multiple GP Farms. It's rare to have multiple city locations with enough food to run multiple uber-GP farms. But yes, if your land allows it, go for it. Just realize that there is a diminishing returns effect in the mid- to late-game when you're running more than 2 or 3 GPP-generating cities. More likely is that you'll have one GP farm and another city getting specialists from wonders.
But to clarify: many people like to have a science city (with Oxford) and a gold city (with a holy shrine and Wall Street). Traditionally, these are cottaged cities with other commerce tiles (gold, dye, etc.), but you can also make also this work with specialists under Caste System or in the late game when you've got multiple specialist-enabling buildings for each kind of specialist. So in this sense, you could have a specialist-powered Science City that acted as a scientist "GP Farm."
Personally, I don't care much about what kind of specialist I get. I find them all useful. About the only time I aim for a particular kind of specialist is when I need one for a corporation.