Some pretty heavy questions pretty fast there!
But I'll do my best to answer.
As to your first question, many other Christian denominations recognize us as a Christian religion. Not just us. It's definitely a split issue among other religions, but at the end of the day, we follow the teachings of Jesus Christ and recognize him as our Lord and Master. We may not agree with how others interpret that, but that's not really our problem. If we were to stop recognizing everybody else as Christians does that make them not Christian? Certainly not. Most countries that recognize us as a religion, also recognize us officially as a Christian religion and in fact, our official name is actually "The Church of Jesus Christ of Latter-Day Saints" which is quite a mouthful and that is why we're frequently abbreviated LDS or we're nicknamed Mormons. We believe in the biblical Jesus Christ, and as part of our faith, we take his name upon us, so it baffles me sometimes why this comes up so often.
For your second question, you are right that we also have The Doctrine and Covenents, and The Pearl of Great Price. These weren't part of the myth per se, the myth being that we somehow replaced the Bible with some other book. The Journal of Discourses is not considered "scripture" by us, but contains talks given by early church leaders which may or may not be inspired.
Related to this, in our church, we have the concept of doctrine, policy, and culture. Doctrine includes a very limited set of things that form the core of our faith and the things we actually believe, and derives from The Bible, The Book of Mormon, The Doctrine and Covenants, and the Pearl of Great Price. These include the things we believe are direct commandments from the Lord, and things we believe He has revealed throughout the ages (ancient and modern) directly or through his prophets. These are the things we believe are unchangeable and perfectly right. Policy covers the things that aren't covered in doctrine. They cover specifics for certain circumstances, and are changeable, but are not allowed to contradict doctrine. They relate to things that our church leaders choose for the church as a whole, but these can be mistakes, as our leaders are mortal men. We trust that if policy ever strays too much, that God will issue doctrine to correct it.
Regarding your third point, it is made very clear in Doctrine and Covenants 132, and even earlier in Jacob 2 that plural marriage is a circumstantial thing only. Specifically only in cases where we believe the Lord wants to raise up seed (or have a lot of children born in a short period of time). We do believe this was commanded in the early days of the church, but was discontinued because any continuation of it would no longer meet the desired outcome. (e.g. if it were continued, and our people were imprisoned, we very well couldn't "raise up more seed", right?) Therefore we believe the Lord put an end to it.
It is important to note that "plural marriage" and "the new and everlasting covenant" are NOT the same thing, and that thinking they are the same thing could easily lead to this mistake while reading it. The new and everlasting covenant refers specifically to our belief in a covenant where marriage can extend beyond this life into the eternities, and not end at death. There's more to it than that, but this is the basis of it. Plural marriage was the conditional practice I explained above.
Hopefully that clarifies a few things! Feel free to ask more. I've had many of these same kinds of questions myself, so I've put some effort into researching their answers.
RE: I'm a mormon so I'll clear up some common myths about us