How is the salutation and signature of a letter written in Latin?

You are not incorrect; but the educated Romans used the third person when writing a letter, for example, 'Neutralitychecker sends greetings to Rose' = Rosae salutem dicit Neutralitychecker . Here are some examples:

The order of the <sender-nom>, <recipient-dat> and the rest of the salutation can vary. The verb dicit is commonly omitted, except in the abbreviated form (D.). Thus there are written salutations such as these:

Cynndarae Apollonius salutem. (To Cynndara, Apollonius sends greetings.)

Areia S.P.D. Apollonio. (Areia sends many greetings to Apollonius)

Omnibus salutem dicit Apollonius. (Apollonius sends greeting to everyone)

For the valediction, a common Latin formula was:

si vales, bene est, ego valeo = If you are sound, that is well; I'm sound.

This was often abbreviated S.V.B.E.E.V.! Another:

si vales, gaudeo. ego valeo recte.

= If you are well, then I'm happy. I am right[very] well.

Latin Salutations

No, not really. Honestly, it makes it more unique. I look at a million signatures a day, and I've seen so many where they just use one letter of the last name, and then loop the letter, followed by scribbles. A signature is usually better this way, because they become much harder to forge.

Well, if you are signing your name it can be written anyway, depending if the letter is in a personal nature. And the salutation of the letter I would think would be written in the nominative or accusitive, but I m not sure.

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twofold answer: 1)legally your signature can be anything you define it as. An X (has to be witnessed), a pretty design (better make sure it's on file with your bank), chinese characters, and yes, your initials with your own personal squiggle. However 2)just remember, the simpler it is, the easier it is to forge.