1). Yes, scripting within Livecycle can be for a single field or even static text, images and other artifacts within the PDF. Really anything, within Adobe's reason, when it comes to scripting.
2). It depends on what you want to do. Things like field validations, calculations and other instances where fields are tied togther really dictate how the script runs.
3). Fields that have calculations or validations with them work in the same, I believe. So for example I have a PDF that I made that is an Excel-type sheet that contains a few hundred cells and every single one has some type of validation or calculation associated with it. I generally run the calculations/validations from the user inputting the data and then after that the script runs, but again, it really dpeneds on what you are doing and with what, so answering some of your questions are a bit difficult.
Javascrip/Formcalc are wonderful tools within PDF, but don't forget the Action Builder (Tools -Action Builder). It is a set of preloaded actions that are turn-key. Just select the cells that will have the action and select the result you want from the preloaded list of actions, using those actions can get you very far, and most of all; they are quick to implement without researching code. So for example, you could use the Action Builder to create an action that checks certain fields and if they are null to return a 1 value to a specific numericField (these could be hidden). Then have a "total" numericField (this would be your counter) that adds all of those fields with the 1 in it. Then create another Action Builder for that "total" numericField and if it is less than 3, display a message box that is a warning.