Only pins can be edited on the schematic, I think (with difficulty). The easiest way is to simply copy the Parts from schematic into a new library (new in the sense of, not where they're originally from, else you'd just change them there, right?), and edit them there. You don't even need to create a file to do this; simply opening a 'New' SchLib and doing the operations will suffice. (Unless maybe, say, on hitting 'Place', it prompts to save, I haven't tried?) But in any case even if a save is needed, it can just be a temporary or local project file.

This is different from PCB components, which can be edited (with some difficulty) on the PCB level via Unlock Primitives.

Only pins can be edited on the schematic, I think (with difficulty). The easiest way is to simply copy the Parts from schematic into a new library (new in the sense of, not where they're originally from, else you'd just change them there, right?), and edit them there. You don't even need to create a file to do this; simply opening a 'New' SchLib and doing the operations will suffice. (Unless maybe, say, on hitting 'Place', it prompts to save, I haven't tried?) But in any case even if a save is needed, it can just be a temporary or local project file.

This is different from PCB components, which can be edited (with some difficulty) on the PCB level via Unlock Primitives.

As for normal workflow, keeping a collection of parts in a master library, or several, or per project (copy and paste from master or diverse sources), or in a database, is the usual way. A related question is whether SCH symbols should have parameters entered per part type (e.g., 1k 1% resistor, 1k 5% resistor, 1.5k 1% resistor, ...), or generic (a resistor; enter parameters for each instance on SCH). Either way gets you where you need to go.