For the fonts, the really cheap and dirty method would probably be to load the names of the fonts you want to use into an array variable in the AppleScript, then get a random index count to grab one of the font names out of that array.
The script as it exists now goes character by character - you'd want to revise it so it went word by word instead, or else you'd end up setting each word's character to one of your random font choices. Instead of
repeat with thisCharacter in (characters of myText)
you'd do something like
repeat with thisWord in (words of myText)
As for loading an array variable in AppleScript - I've not done that before, but it's probably something like:
set myFontArray to {"Papyrus", "Arial", "Comic Sans"}
The curly braces are necessary, as it appears that AppleScript supports lists rather than arrays (a minor but not entirely unimportant detail). Anyway, from there, you'd grab one font at a time, randomly, probably like this:
set myWordFontNumber to random ( length of myFontArray ) - 1
set myWordFont to item myWordFontNumber of myFontArray
You do the first line to get a random number based on the number of items in your list of fonts. You subtract 1 from it because the count on the actual list begins at 0 rather than 1, which means that sometimes you'll get a random number that's actually 1 larger than the number of items in the list, and you'll never see the first item (which is at position 0). This is a very old-school gotcha when working with arrays and lists - a ten-item list will count from 0 to 9, not 1 to 10.
From there, you'd set the given word in your text frame's font to the name of the font you pulled out of the myFontArray variable. You'll want to make sure that the font names you load into your list are the actual names of the fonts you're working with - the examples I used here probably won't work.
Please note that this is just a high-level gloss of what you'd need to do in order to modify the script. You'll have to hit the AppleScript documentation (and InDesign's scripting documentation) to get the precise syntax.
