As far as question #1 and #3, there is this:
"According to the guidance of the House of Justice, letters received at the Bahá'í World Centre are sent to various Departments, according to their topic. For instance, all the letters related to the Research Department are sent to that Department so that, with the guidance of the House of Justice, appropriate responses could be prepared which are then sent out through its Department of the Secretariat."
As far as your questions #2, #3, and #4, there is the following guidance regarding the difference between letters on behalf of the House (from the Secretariat) and those written directly by the House of Justice (and info on who prepares them):
As to whether there is a distinction between correspondence from the World Centre that has been signed "The Universal House of Justice" and that signed on behalf of the Secretariat: In brief, the manner in which each of these letters is prepared depends upon the contents of the letter. Drafts of letters which contain newly formulated policies are consulted upon and approved during a meeting of the House of Justice; correspondence dealing with previously enunciated policies, or with matters of a routine nature, are prepared, as delegated by the House of Justice, by its Secretariat and initialed by at least the majority of the members of the House of Justice before being dispatched. All letters written over the signature of the Department of the Secretariat are authorized by the Universal House of Justice.
So it would seem to me that something like The Promise of World Peace which was signed by the Universal House of Justice went through a full review by the entire membership, whereas others may only have been a majority. Since 'Abdu'l-Baha stated "That which this body, whether unanimously or by a majority doth carry, that is verily the truth and the purpose of God Himself" (WT 19
), it should make no difference as far as authoritativeness, but perhaps there is a difference here similar to that with letters by or on behalf of Shoghi Effendi:
Although the secretaries of the Guardian convey his thoughts and instructions and these messages are authoritative, their words are in no sense the same as his, their style certainly not the same, and their authority less, for they use their own terms and not his exact words in conveying his messages.
(25 February 1951 to the National Spiritual Assembly of the British Isles, cited in http://bahai-library.com/uhj_letters_behalf_guardian#s2
A related issue you may also be interested to know about is for materials prepared by the Research Department (and presumably other departments). Here is the guidance on these types of documents:
As to whether the materials prepared by the Research Department constitute the authoritative word of the Universal House of Justice on a particular subject, as raised in your third question, the House of Justice indicates that such materials, though prepared at its direction, represent the views of that Department. While such views are very useful as an aid to resolving perplexities or gaining an enhanced understanding of the Bahá'í Teachings, they should never be taken to be in the same category as the elucidations and clarifications provided by the Universal House of Justice in the exercise of its assigned functions. However, the House of Justice chooses to convey the materials prepared by the Research Department to the friends because it wishes them to be thoughtfully attended to and seriously considered.
A similar quotation is found at http://bahai-library.com/uhj_letters_behalf_guardian#s3
I've linked to these letters from http://bahai9.com/wiki/On_behalf_of_the ... of_Justice
and you may also be interested in http://bahai9.com/wiki/On_behalf_of_Shoghi_Effendi
I'm not sure what you mean by "Or there is another signatures under the opinion of Universal House of Justice itself, like in Messages."... Can you give an example? I guess you mean letters like those with the Guardian where one part is on his behalf and another is in his handwriting? I don't recall if there are such examples by the House of Justice; from what I recall, it is just one or the other.