Obama is definitely an American citizen. Any presidential candidate is vetted carefully by the Secret Service, the NSA and who knows whom else.
I personally believe that Obama was born in Hawaii, and is a US citizen, but presidential candidate citizenship (or anything else) is not vetted by the Secret Service or the NSA. Each state is responsible to make sure that those who are on the ballot for president in that state is constitutionally qualified, and the Congress can also entertain objections regarding constitutional qualifications when the Electoral College convenes to vote. Presumably, the US Supreme Court could rule on this as well.
Obama is most likely not a Communist. Besides the fact that it is difficult to prove he is or he is not, the term Communist is very judgemental in the USA. It doesn't simply mean left-winged or lover-of-Marx, it basically means: Anti-American. This is a leftover from 50 years of Cold War and the accompanying propaganda.
Whether Obama is a socialist or a communist has little to do with whether he is anti-American. It has to do with his beliefs about structure of the economy (government controlled vs free markets, etc). I don't think people are as naive as they were in the 1950's. Very few people in world (anymore) are completely for complete government control, or completely free markets with zero regulation, so this is always a matter of emphasis and application to specific circumstances and policies.
Nobody is trying to make a criminal case against Obama. These accusations are character attacks. They are meant to cripple his presidency in the short term, by rallying support against any governmental action he takes because it must surely be the deed of a Muslim America Hater. In the long term, it's meant to deny him a second term and to burn the Democratic party.
It is part of the strategy of neo-conservatists to outright alienate the third of the American people who would identify themselves as liberal.
Again, it seems very naive to suggest that liberals are going to abandon Obama on the basis of claims about his religious or ethnic background. Liberals may have some doubts these days about his liberalism, but surely they already know about his background.
From ages six to ten, Obama lived and attended school in Jakarta, Indonesia (the largest Islam nation in the world), and was "exposed" to Islam by his step-father, a practicing Muslim. It seems just as foolish to deny this, as it does to make too much of it.
Personally, I think Obama is an atheist (or at least agnostic), but not sure why that is of paramount concern. Granted, there are some on the left or right who vote for candidates based on their religion, whether it be Protestant, Catholic, Mormon, Jewish, Muslim, Buddhist, etc, but most people vote based on policy matters (especially those that effect their own pocket-book).