What is the name of the Eternal Father worshipped by Latter Day Saints?

Since this came up a lot in the comments to the other answer, here what was said in 1916 in an exposition of the First presidency regarding the mentioning of the different father roles Jesus Christ and God the Father have:

Scriptures embodying the ordinary signification—literally that of Parent—are too numerous and specific to require citation. The purport of these scriptures is to the effect that God the Eternal Father, whom we designate by the exalted name-title “Elohim,” is the literal Parent of our Lord and Savior Jesus Christ and of the spirits of the human race. Elohim is the Father in every sense in which Jesus Christ is so designated, and distinctively He is the Father of spirits.

Wikipedia as well as FairMormon.org cite this to source where the usage of "Elohim" for God the Father is coming from.

From the Fairmormon.org article (mind you, this is not an official church site, but I somewhat agree with their reasoning).

The LDS use of the name titles Elohim and Jehovah to designate God Our Heavenly Father and His Only Begotten Son, Jesus Christ respectively is not meant to insist that this is how these titles were always used anciently, including in the Holy Bible. Rather, these titles are a naming convention used in the modern Church for clarity and precision. Since Christ may be spoken of as "the Father" in a great many senses, the modern Saints use these name-titles to avoid ambiguity, regardless of which 'role' of a divine Personage is being discussed.

Since this terminology was not standardized for convenience and clarity prior to the twentieth century, readers are cautioned not to expect the early writings of the Church to always reflect this practice, which arose only decades later. Likewise, attempting to read the Bible as if its writers followed the same modern practice is anachronistic, and may lead to confusion and misinterpretation.

Although Elohim is understood and used in the Church of Jesus Christ of Latter-day Saints as the name-title of God the Eternal Father and the name Jehovah is reserved for His Only Begotten Son, Jesus Christ, this has not always been the case. Nineteenth-century Mormons—including Joseph Smith, Brigham Young, and John Taylor—generally used Jehovah as the name of God the Father. Latter-day Saints also recognize that the Hebrew word Elohim was used anciently as a generic word for "god."

LDS are not Jehovas witnesses, we don't care so much what the "real name" of God is. We take what is revealed and acknowledge that there is yet much to be revealed. We are fine with "name-title". If you insist on some "proper name" and don't want to count Elohim, then we don't know the name.

From wikipedia "Name":

A name is a term used for identification. Names can identify a class or category of things, or a single thing, either uniquely, or within a given context. The entity identified by a name is called its referent. A personal name identifies, not necessarily uniquely, a specific individual human.

A name is something that identifies someone or something.

So, to summarize, not everywhere in the bible where it says "Elohim" is necessarily a reference to God the Father, not necessarily every instance of "Jehova" actually refers to God the Son. And not necessarily are older LDS writings consistent with newer ones on the usage of Jehova and Elohim.

With regard to your other questions:

Is God the Father creator of all creation?

This is what he said in Moses 1:

33 And worlds without number have I created; and I also created them for mine own purpose; and by the Son I dcreated them, which is mine Only Begotten.

34 And the first man of all men have I called Adam, which is many.

35 But only an account of this earth, and the inhabitants thereof, give I unto you. For behold, there are many worlds that have passed away by the word of my power. And there are many that now stand, and innumerable are they unto man; but all things are numbered unto me, for they are mine and I know them.

So, we explicitely do not know much of anything beyond our earth, but we know that we are not the only earth.

What has been revealed is what we have to do in order to, eventually, become like God (D&C 76:50-62). It includes:

• being righteous (too many scriptures to cite, but this is the whole point of the laws we are given and the atonement to free us from sin)
• resurrection to obtain an immortal body (atonement makes this a free gift) (for example D&C 138:17)
• new and everlasting covenant of marriage (D&C 131:1-4)

We know God is righteous, and all the good attributes you want to fill in here. We have to become, eventually and through the atonement, like him in this regard.

We know he has a body because he has shown himself in the first vision (Joseph Smith-History 1:17, D&C 130:22-23). Jesus has gained his body through resurrection, we will too. God the Father?? This is one point made in the King Follet discourse linked by the other answer.

We need to be married to have children? Does this tell us something about God? We are never explicitely told in scripture, but it would be very weird if we are the same as God (created in his likeness), but different in this aspect.

The King follet discourse linked by the other answer shaped our view of God regarding these matters, and is an interesting read, but be aware that Joseph Smith tends to use strong words.