The Pledge of Allegiance is not mandated by the Government.
also, the paper and coin currency that you carry is issued by the Federal Reserve (despite its name, it is not controlled by the Government). I believe actual US Treasury bonds (issued by the US Govt) do NOT say "In God We Trust".
Both of these examples are perfectly legal. And, in fact, the Establishment Clause prevents the government from establishing a state church, but not from publicly acknowledging a God (or even Gods). Separation of Church and State does not appear anywhere in the Constitution.
"say a president decided to put forth laws to ban the above things mentioned because they were considered unconstitutional"
President's don't put forth laws. They can ask Congress to come up with one, but all legislation must start in the House and Senate. A President making a law and passing it without Congress IS unconstitutional. Executive Orders have little legal power and can be overridden. They are in no way considered laws.
Marriage is a legal term with a legal definition. In order to be considered married by the state, you must apply for and be issued a marriage license. The religious ceremony involved is only tradition and for show. You can have a wedding and not be legally married. Conversely, you can become legally married and never have a wedding ceremony.
EDIT: The Federal Government does not have an all encompassing definition of marriage, rather, each state makes its own and the Feds back them up. If a state decides to specify that marriage is between one man and one woman, even if the definition agrees with some religions, it is not in itself establishing a religion or "playing favorites".
I'm not saying that gays shouldn't be allowed to get married, though.