Good question. They often teach words here, where the English is ambiguous, either because it simply means two things, or because it means different things in American and British English.
Yes, it covers both the character and the epistle.
In case you have not been told yet, for the names of the letters themselves we just use the English names, but we are always tolerant of American, English and Scottish variants, so
- h = aitch, haitch
- j = jay, jie
- z = zed, zee
Gaelic society was not historically literature-based, so no there is no special phrase. I can't find one in English either, although we do have red-letter days and Blackletter is a script and hence the name of some fonts. Gaelic script is not closely related.
Note that although letter often occurs in the English version of Gaelic placenames, it has nothing to do with writing. It is from leitir 'hillside'. You can find a long list of examples if you search for leitir at faclair.com, making sure you select the 'part of word' option.