These questions are getting way out on the edge of Mormon metaphysics but since they’re asked sincerely I’ll give them a try.
Please note that the following is just my opinion. Although official Mormon doctrine clearly states that faithful children of God can become like God, very few details of that God-like state are given**. However, the ability to bear spirit children is clearly indicated.
This one is a bit unclear. There are two conflicting principles – 1) the obligation for us to worship God never ends vs. 2) the belief that we will be in a state like God’s.
So who would our spirit children worship? The notion that any being should worship anyone other than God, much less ourselves, sounds blasphemous even by Mormon standards. IMO our spirit children would still worship God.
This one is more straightforward. We believe that truth exists eternally, independent of God, and that God is himself obedient to this eternal truth. In a sense, we attain godhood when we become fully allied with this truth. In this case, the moral code is derived from these eternal truths and we would “just pass on the standard moral code of Mormonism”.
**Another common Mormon belief is that if it’s really important we’ll get more information. We don’t really need details on this subject to know what our duty here and now is. We are to love God with all our heart, soul, might and mind, and our neighbors as ourselves. The detailed mechanics of the afterlife will certainly become clear as we pass into that phase of our existence. (This is one reason why Latter-day Saints tend to be reticent when questioned on these subjects – it sometimes seems like unimportant speculation when the important question is how do I live today to please God?)
At present, Mormon metaphysics is limited to our human (but not necessarily mortal) existence. We believe we came from God, as his spirit children, and we believe that we can become like God, with spirit children of our own. Where God came from and/or the nature of the existence of our spirit children is not specified. Logical inferences and extrapolations of these principles are frequently made but they are, officially, just speculation. With that disclaimer, let me say that the philosophy behind Mormon theology definitely favors an infinite regression over ex nihilo creation.
For those who are particularly interested, one of the best resources I know of is a short book entitled The Theological Foundations of the Mormon Religion by Sterling McMurrin. Unfortunately, I don’t know whether it is still in print. My copy is almost 30 years old.