Some churches teach that God doesn't communicate with man anymore, or that there are some kinds of limitations on interactions between God and man. My belief is that God is not limited in that way, and still communicates with us, and calls prophets, and is as concerned with us as He ever was. I believe that there is still revelation, and that the same church and the same gospel that existed from the time of Adam was restored to the earth. Please read this account of how the gospel was restored:

http://scriptures.lds.org/en/js_h/1/16-17#16

The highlighted part tells of what we refer to as "The First Vision," in which God the Father and Jesus Christ appeared to Joseph Smith. If you actually saw God appear to you, then you would be a sure witness, as sure as those who lived in Jesus's time and saw his miracles. There are other miracles that happen in our time too, some large and some small. People are healed of incurable illnesses, or are given what they need when there was no hope of finding it. It might be something so simple as losing something, searching everywhere for it, praying, and finding what you had lost (I have had that happen more than once). If you ask, you can receive your own witness from the Holy Ghost. God doesn't need to come down and appear to each of us, but we can all have that feeling in our hearts if we ask for it that will tell us what is true. I have felt it when I asked, more than once.

If you read more of that passage (scroll up as well as down), you may find some answers to more of your questions. I'm not sure that I am on the same page with you about "the age to come," but regarding the unpardonable sin, I believe that the age to come refers to after death - the next life.