beefily/billowy, trollied, tux, ebb.
There are two 7-letter words with letters in ascending alphabetical order, beefily and billowy.
If you want strictly ascending order (no repeated letters), the longest is six, found in abhors, almost, begins, biopsy, chimps, chinos, and ghosty.
For reverse order, the longest word is trollied, with eight letters.
For stricly descending order, the longest words are seven letters long, as in sponged and wronged.
The last word, alphabetically, to be arranged in ascending alphabetical order is tux. If you don't like that word, a derivation of 'tuxedo,' the next last word is sty.
The first word alphabetically whose letters are in descending alphabetical order is just a. If you want a less trivial word, ebb has three letters.
If you want a word with more than one letter that doesn't repeat any letters, the first alphabetically is fa. If you don't like that, try fed.
Charlie wrote a program that produced a more complete list, seen here.