You are very right in that things need to change. If they don't, nothing interesting happens and we as programmers don't get paid :p. State changes are typically moved to the edges of a program. Functional Core, Imperative Shell is the name for that particular architecture style.

FCIS can be summed up as: R->L->W where R are all your reads, L is where all the logic happens and is done in the FP paradigm, and W are all your writes. Do all the Reads at the start, handle the Logic in the middle, Write at the end when all the results have been computed. Teasing these things apart can be a real pain to do, but the payoff can be quite significant. You can test all your logic without needing database or other services up and running. The logic in the middle becomes less brittle and allows for easier refactoring as there is a clear separation between R, L and W.

For your first question. Yes, and I might misunderstand the question, so give me some rope to hang myself with will ya ;). I would argue that what you really need to care about is the data that you are working with. That's the real program. Data comes in, you do some type of transformation of that data, and you write it somewhere in order to produce an effect (the interesting part). The part where FP becomes really powerful, is when you have data that always has a certain shape, and all your functions understands and can work with the shape of that data. When that happens, the functions starts to behave more like lego blocks. The data shape is the contract between the functions, and as long as they keep to that contract, you can switch out functions as needed. And so, in order to answer the question, yes, you do need to understand the entire program, but only as the programmer. The function doesn't, and that's the point. When the code that resides in the function doesn't need to worry about what the state of the rest of the program is, you as the programmer can reason about the logic inside, without having to worry about some other part of the program doing something that it should do that at the same time will mess up the code that is inside the function.

Debugging in FP typically involves knowing the data and the function that was called. You rarely need to know the entire state of the program.

Does it make sense?