There is a single reference to Script Assistant in Apple Docs: AppleScript Language Guide. It merely state the obvious:
“You can also turn on or off the Script Assistant, a code completion tool that can suggest
and fill in scripting terms as you type.”
What key do I press to accept the word being suggested? (…so much for user friendly the arrows and tab key don't work).
AS is one of the worst learn-a-new-programming-language experiences I've had. Cut and paste two line demo code from Excel 2004 and Applescript User Guide and it fails over and over again. Sytax is weird, verbose and non-intuiative for me at least.
The keys they chose definitely aren't very intuitive, but they are explained in the AppleScript Editor help - escape will accept the current completion, and as long as an ellipsis is next to the cursor there are multiple possibilities that can be shown by pressing option-escape (from there, a more normal up/down arrow and return select the choice).
The scripting dictionaries (if implemented at all) are entirely up to the developer, so the terms for any given application (or application version) will usually be different than those for another application, so you would need to check the dictionary by opening it in the Script Editor to see what the exact terms and their usage are.