Citizens working the individual tiles are what bring in the resources that tile provides (in terms of food, hammers, commerce). Simply having a four-food farmed flood plains tile in your city's fat cross will not provide any extra food - working that tile with a citizen will. In this manner, you will be put to decisions often when you micromanage your cities' production: do you want to bring in more food for growth (/work more farms), more hammers for faster production (/work more mines), or more commerce to speed up your tech and maintain your economy (/more cottages)? This provides you with a lot of flexibility and options, but it will become more intuitive and easy to manage over time.
The net result of all this is that for a given city, the total yield per turn will be limited by the number of citizens you have and can therefore allocate to working tiles. As such, typically you want as many citizens as possible, up to the point where you reach your happiness (or in some cases, health) limits (i.e. the point at which the number of

= the number of

at the top of the city screen - more than that and you'll get resisting citizens, who bring in
nothing but still eat two food per turn, the ingrates

). The more [non-resisting] citizens you have, the more tiles you can work, and the more resources you will bring in per turn (please note that in this I am using the term 'resources' as a blanket term for food, hammers, and commerce, rather than the more common reference to specific strategic, luxury, or food bonus resources).
The caveat to all this is that you [typically] need to feed all of those citizens. Each extra person in your city will consume two food per turn. Therefore if you have say five citizens in your city, the city will be consuming ten food per turn just to stay fed (you can temporarily shortchange this in dire or unusual circumstances, but if you run a food defecit for too long you will start to lose population). The idea, then, is that you will have to balance your desire to work more productive or commercial squares with your need to work enough food to maintain, and preferably grow, your population. As you get more familiar with the game mechanics this will become second nature, but it will always be a decision you will be able to control if you wish. When cities are nearing their happiness limits, you may want the city governor to emphasize production or commerce (or both) rather than food; conversely when you are looking to grow a city quickly you may want the governor to emphasize food exclusively or some combination including it (you can certainly do this manually as well, but the city governors (lower right of city screen) can automate some of the process for you so you can focus on the big picture while still learning the game).
So essentially, regarding question two, the tile yields are what they are, and it's just up to you to determine which combination of tiles within your fat cross will provide the most direct benefit to your city at any given time. The one exception to this would be cottages, which do actually grow slowly over time, but only if/while they are being worked by citizens.
As to the scenario in your first question, you would probably avoid a setup like that for all but one city in your empire (unless you are running a specialist-based economy). For most cities, it would not be productive to have so much excess food that it would get to that point, as you'd be looking at almost exclusively farms and very little production or commerce. Typically (and this will get easier with time as well) you would try to balance things out (in the late game) such that you are bringing an amount of food either equal to or just barely over the amount necessary to feed the maximum number of non-specialist working citizens. An equivalent amount would suffice, but I personally like to try to have +2 food with all tiles worked, at least until the city caps out, so that growth is not quite so slow at the end stages and you have a slight buffer in case you get an angry citizen that needs to be fed.
One very high-food city in your empire can become a GPP (great person points) city, and run a lot of specialists in order to generate great people (and typically build the national epic in that effort as well), but running heavy specialists in multiple cities is less efficient in generating great people and therefore typically avoided unless a specialist-based economy is your specific aim. Outside of this city, most remaining cities will be focused on production-heavy tiles (for production-oriented cities) or cottages and commerce-heavy tiles (for commerce-oriented cities), and will not have a huge food surplus to overgrow the amount of workable land they have by much. Specializing cities is not necessarily something you need to focus on right away anyway, but just FYI for down the road you can potentially differentiate between focusing on production or commerce in order to get your empire up and running more quickly and efficiently (e.g. a high-production city can skip libraries, markets, and the like and just focus on producing troops (after building a barracks typically), whereas a high-commerce city can ignore a barracks and troops and focus on working cottages and whipping slaves to complete the commerce-boosting buildings).
Oh yeah, and 'pop', used around here, typically either refers to 'population' as you mentioned, or whipping citizens while running the slavery civic to rush prodution (via the upward-pointing arrow above the city governor area). In the latter instance, "pop & chop" refers to the two methods of early-game production rushing - either through slave whips or forest chops. It can also sometimes just generically refer to completing something ("just popped an axeman" might not imply slavery depending on context), or even getting a freebie from a goodie hut ("I popped 'Animal Husbandry' from a hut!").
Wow, did that get verbose - I'm spoiler-boxing this so as not to clutter up the thread too much. The lesson here is: "Don't ask open-ended questions to a bored engineer who's stuck at work".

Hope this helped some.