Do Mormons believe in God?
Definitely
Is their understanding of the nature of God substantially different from mainsteam Protestantism or Catholicism?
Yes, but the concept that the Godhead consists of 3 separate and distinct beings, while a minority belief, is certainly not unknown in both ancient and modern Christianity (see..Jimmy Swaggert)
Do Mormons believe that they can become Gods?
Certainly. And they are not at all shy about telling you about it, either. It is not a doctrine shrouded in mystery or one of which they are ashamed. But, most Mormons understand that you don't lead with that doctrine when teaching because it is usually misunderstood. So most prefer to talk about it only with those that have some basis in the restored Gospel.
Do Mormons believe that non-Mormons all go to hell?
No, not at all. In fact Mormons don't even believe in hell in the traditional sense. Mormons believe that nearly all people will recieve a certain degree of glory in the hearafter, in direct proportion to their goodness and obedience to the Lord. Those who most perfectly follow God's commandments will recieve the highest degree of glory, which includes the concept of "Eternal Progression". Those who are less valient will receive lesser glories.
All in all, the restored Gospel is the MOST hopeful, most optomistic gospel on earth.
And why we may believe others are wrong in their beliefs, we are great supporters of freedom of conscience and freedom of belief, and are eager to support government that allows the greatest degree of freedom avaialable to the children of men.
Leave it to LDS theology to teach opposite what Christ said: "wide is the road to destruction; narrow is the way to life." "Destruction" has now been redefined as "eternal life" (just a "lesser glory").
Leave it to the reps of the one below to change the Detour Sign from "All Roads Washed Out: Only One Way to go" (John 14:6) to one that counters Hebrews 9:27: "There's many glories, many degrees of glory, multiple ways of getting there--even accepting the gospel post-death, provided somebody's been baptized in your behalf--and most of you won't be effected by the 'all-roads-washed-out' reality" 'cause it all depends on your valience, your worthiness, and ALL you can do (Book of Mormon, 2 Nephi, teaches that grace only kicks in AFTER ALL YOU CAN DO).
This is kinda like the Mormon doctrine that Adam & Eve's fall was an "upward fall." Rape, mass murder, wars, incest, abuse, exploitation, oppression...etc. all has been redefined by LDS theologians as a fortunate set of circumstances...as man's "upward progression & exaltation" would not have been possible had Adam & Eve not fallen.
Do Mormons believe that they can become Gods?
And the serpent said unto the woman, Ye shall not surely die: For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.
(Gen 3:4-5)