I´d say "....to deliver mail more quickly...." Mail is uncountable. You can have three dollars, but you can´t have "three moneys". It´s the same thing with mail :)

No. Mail is considered a non-count noun. You may use "letters" in this place, or "pieces of mail" if you want.

The mail delivered through the post office is a mass or uncountable noun and thus has no plural form. I received mail (one letter) or mail (two letters and a magazine). In the world of computers we are starting to see the term e-mails in reference to receiving several e-mail messages. Given the evolving nature of language, e-mails seems to be turning into an acceptable word that is interchangeable with e-mail messages.