No, Yes, No*.
This would be the most likely public response from most Imams, and should be considered a stereotypical response, and the stereotypical response from Christian priests was the same until the sound of the audience's laughter basically drowned them out. Which was... sometime in the last twenty years, after over a thousand years of well documented Christian child sexual abuse. I do not mean to set up any false equivalency here, instead, I am trying to confirm that yes Islam has a very large hypocrisy problem regarding homosexuality, but @Wanderfound is right - it is not something that sets them apart from other religions (I could bring in several more).
This is a fundamentally false claim. Sharia literally means religious law. The mainstream of conservative thought in the United States is openly and loudly in favor of religious law taking precedence over secular law. To claim otherwise is either the most blatant propagandizing against one specific religion's laws, or against one specific language (arabic) that uses the word sharia to describe something we all know mainstream conservatives consistently support - putting their religion above the concerns of atheists and other religions.
Haha! Good luck with that. Abundant technical and financial assistance given to such countries by the US government and other such "progressive" and "secular" nations means that you will have very little access, unless you are willing to risk your life and wealth to do so. However: If you are really serious, and have the money and time to the travel, I can hook you up.
My religion was performing marriages for homosexuals in violation of US law for decades, while secular authorities would not. Just as @Mister44 is overstating the role of Islam in this, you are overstating the role of religion. There are intolerant, gay-hating religions everywhere, but those are not the only religions that exist. There are life-affirming, non-dogmatic, even atheistic religions that you can join today, that are a positive force for good in the world.
* Actually Yes but only when the form of Sharia recognizes primacy of secular law, which is almost never and nowhere, so for all practical purposes No.