Ben Carson, Islamic Law & the U.S. Constitution; Compatibility and Conflict

ASA,

There's been a lot scurrying and "clarifying", in response to comments made by Dr. Ben Carson, regarding his concern about supporting a Muslim for president of the United States, based on the notion that "Sharia Law" is incompatible with the U.S. Constitution. .

As expected, the reaction from some Muslims was one of immediate outrage, with some calling for Carson to withdraw his candidacy. 

In the aftermath, besides Dr. Carson stating that he wouldn't support a Christian who wanted theocracy (Christian Sharia), as this would put him at odds with the same Constitution.

One of the Muslim respondents has gone on record to defend Dr. Carson, saying that "a Sharia promoting Muslim cannot be the President of the USA, with its wonderful Constitution".

Hold on,we haven't even put a candidate out there, and already, we're dictating what that candidate can or cannot do!

A few thoughts come to mind, when I try to assess these statements and positions:

1) Does anyone of us here, know the Constitution from a scholarly standpoint, to qualify that this and Islamic Sharia are by design, incompatible?

2) If a believer, be he or she Muslim or Christian, avers that their Books are the irrefutable words and mandates from God, why would that person defer to the Constitution, outright?

3) What is Sharia in the first place? Are the images we've seen of "Sharia" in action, much less the penal aspects of it, fair and accurate examples?

4) Are Muslims conceding that the Qur'an and Sunnah are not consistent with the Constitution, which would support Dr. Carson's arguement? 

5) Does the Constitution provide an opportunity for "Sharia Law" to be woven into its fabric?