As to your first point, the US government is bound by the constition, and legal opinion is split as to the constitutionality of a ban on all Muslims. http://www.wsj.com/articles/BL-LB-52706
As to the second point, whether or not someone is a Muslim gives you essentially zero information as to whether or not they are a terrorist. (Trivially, it makes them more likely to be an Islamic terrorist, just as Hindus are more likely than non-Hindus to be Hindu terrorists. But since such a miniscule fraction of Muslims are terrorists, applying additional screening to Muslims would make no difference.)
As to the second point, whether or not someone is a Muslim gives you essentially zero information as to whether or not they are a terrorist. (Trivially, it makes them more likely to be an Islamic terrorist, just as Hindus are more likely than non-Hindus to be Hindu terrorists. But since such a miniscule fraction of Muslims are terrorists, applying additional screening to Muslims would make no difference.)