As simple as possible to summarize the best way you can, first, please. Feel free to expand after, or just say whatever you want lol. Honest question.
So, for the sake of this post isn't "I'm trying to convert you to my religion" I'm going to try and summarize our points of belief while more or less answering your question, and I'm not doing it out of a debate, but merely to answer you :)
It's not really "we think we're lucky or better than anyone else" hell we actually believe that God is a God of fairness that doesn't value one person over another. Ie. "We are all his children and he loves us equally" is a core belief we hold. And as apart of that belief, we firmly hold it true that God will ensure that all his children who lived or died without hearing his gospel will have the opportunity too. That's point 1
Point 2. Yes you can most certainly have spiritual experiences outside of the LDS faith or any faith for that matter. We tend to refer to that as "The light of Christ" but for a summarized explanation. We basically summarize that as, a testimony of truth wherever it may be found God will bare witness of it.
And I also tend to lean towards a lot of Buddhist tenants myself btw. The concept of a state of being called Nirvana, that life is suffering (Though I know that's not exactly what he said) and a few other ideas they hold I agree with.