No, I don’t think “self-explaining” is a very apt word choice for referring to a letter attached to a transmission or forwarding message. Much more appropriate and widely used is the word “self-explanatory,” which means “explaining itself” or “capable of being understood without explanation.” In any case, the sample sentences you provided that use “self-explaining” and “self-explanatory” are wordy and stuffy bureaucratic clichés, and I really wouldn’t recommend their use. Specifically, I find the phrases “for your information and action” and “for your information” objectionable because they state what’s already very obvious—for indeed, what else is a letter designed for but to inform somebody and make that somebody act on that information? It actually insults the intelligence of the receiver of the letter! So I would suggest this much simpler version instead:
“Please find the attached self-explanatory letter.”
