Are U.S. politicians assumed to be Christians (no matter which sect)? Is it possible for an atheist or Muslim believer to become US president? Are there any legal obstacles?
There is no law in the US that says that holders of any office need to be of any particular religion, in fact, any such law would be unconstitutional.
Being an Atheist of Muslim might fewer people vote for you, but if you do get enough votes, there is no law that says that you can't hold office due to religion.
Article Six of the US Constitution prohibits the federal government from rejecting a duly selected politician from being installed into the seat for which he was elected, on the basis of religion (or lack thereof).
But it does not prevent localities from setting rules of their choice for becoming a candidate in the first place, which is obviously a pre-requisite for being selected. (Note that in practice these offices are now filled by election, but this wasn't historically the case.)
In most cases those rules consist of requirements on age, residency, and a criminal record clean of felonies. In addition, being listed on the ballot, which is a de facto if not de jure prerequisite to election, collecting a certain number of signatures. But there surely are weirder requirements in some jurisdictions.
In theory it is possible, there are no legal obstacles (at least not for the USA as a whole).
In practice, at least right now, it is completely impossible for an atheist to be elected president, given that about 25% of Americans think that "Only politicians who believe in God are suitable for public office", about 50% find atheism "threatening", and (admittedly some time ago) elected as president someone who publically stated that he doesn't consider atheists citizens.
Yes. As the vast majority of Americans are Christian, it is safe to assume that a given politician is also Christian, in the absence of any claims otherwise.