Good question.
It has been talked about for the MMO plans to give each language its own typeface, which would appear in-game when using the language system. This would ultimately be a matter of time and technology, but it is theoretically possible. Anyway, that would be meant to reflect the fact that each language would, in fact, have its own alphabet in an IC sense, each being distinctive and unique.
So yes, elvish would have its own alphabet. Dark elvish would have a similar but distinct alphabet. Dwarvish, gnomish and most other languages would have their own distinct set of character glyphs. There would also be a mapping of the glyphs of one language into those of another, much as is done when teaching the sounds of an alphabet like Cyrillic to someone used to a different alphabet, or like which is done for languages like Chinese or Japanese when their words are converted into the Latin alphabet, for example. These may not be perfectly exact, of course, but suffice for certain purposes. Given NWN's limitations, it's safe to assume what is translated by the in-game mechanisms is the latter case.
So yes, there are different alphabets for different languages, and it is appropriate to RP learning the letters as well as the spoken form of the language.
Regarding the creation of such, that would be a matter to take up with Leanthar and/or EdTheKet. As with other lore-relevant content created for Layoanra, creation of an alphabet for each language would entail signing a legal document. What I don't know is if this is something we are still looking to pursue.
In the absence of any reference on glyphs, it would be OK to make some stereotypical assumptions as to their look (i.e. elvish is flowing and almost artistic in its own right, dwarvish is more angular and easily carved in stone or metal, etc.). The safest thing is to just keep the details vague and RP the practice of forming the letters.