Yes. 100% accurate, although this needs to be followed through that the government must also be protected from religion. If ANY form of religion is favored over another, than there exists oppression against the second religion. Therefore, in order to protect every religion, there can be no connection between Church and State (which I understand is unfortunately not the case anymore). I absolutely agree that atheism should also not be taught in state schools (even though it is not a religion by any means).
There was absolutely no discussion in the founding documents about "protecting govt. from religion" - ALL of the discussion and concern had to do with protecting religion and the people from the government! The Constitution established a civil government (no constitutional possibility for a theocracy even is someone wanted to establish one) based upon judeo-Christian principles (derived from the writings of Locke, Montesquieu, Puffendorf, and Blackstone). They did not want a repeat of the Church of England's (THE state church) persecution of other denominations (remember the pilgrims?). The founders did believe that one "religion" not be favored over another, but in the correct context, they meant "Christian denomination" since America was 99% Christian at that time. Let's be historically accurate about the intent of our founders. Nowhere in any founding document is the term "separation of church and state" mentioned. Nowhere.
Yes, B. Rabbit. This was a major concern of the Framers, who had the European experience of the horrific religious violence and warfare of the 16th century vividly in mind: Monarchs kept "establishing" the religious sect of their preference as the "national church," and all the folks not in the "official" church were often persecuted, exterminated, church property seized, etc. The Framers sought to make sure that could never happen in America.
On the bright side, the ensuing religiously-motivated emigration (e.g., the English Puritans, et al.) to the shores of the New World made for the birth of the American nation.
So it is not at all surprising that the first phrase of the First Amendment's religion clause forbids Congress to establish a state church. Yet the second phrase, it seems to me, does not banish God from the public square. Indeed, in the early Republic, there were many national days of public thanksgiving declared -- the thanks being given expressly understood to be thanks to God.