Both statements in the title have been claimed about Jefferson. Was he a Deist? That is, did he believe God had no dealings with the Universe or the beings in it? Consider what he said in his second inaugural address: ” I shall need, too, the favor of that Being in whose hands we are, who led our forefathers, as Israel of old, from their native land, and planted them in a country flowing with all the necessaries and comforts of life; who has covered our infancy with his providence, and our riper years with his wisdom and power; and to whose goodness I ask you to join with me in supplications, that he will so enlighten the minds of your servants, guide their councils, and prosper their measures, that whatsoever they do, shall result in your good, and shall secure to you the peace, friendship, and approbation of all nations.” That is not Deism! That is exactly what the Bible says about God – He is very much involved in the Universe and the beings in it!
Did Jefferson believe that government and religion should be kept separate? Notice what he said in his first inaugural address: “Let us, then, with courage and confidence pursue our own Federal and Republican principles, our attachment to union and representative government. Kindly separated by nature and a wide ocean from the exterminating havoc of one quarter of the globe; too high-minded to endure the degradations of the others; possessing a chosen country, with room enough for our descendants to the thousandth and thousandth generation; entertaining a due sense of our equal right to the use of our own faculties, to the acquisitions of our own industry, to honor and confidence from our fellow-citizens, resulting not from birth, but from our actions and their sense of them; enlightened by a benign religion, professed, indeed, and practiced in various forms, yet all of them inculcating honesty, truth, temperance, gratitude, and the love of man; acknowledging and adoring an overruling Providence, which by all its dispensations proves that it delights in the happiness of man here and his greater happiness hereafter—with all these blessings, what more is necessary to make us a happy and a prosperous people?” He ended the first address with the words, “And may that Infinite Power which rules the destinies of the universe lead our councils to what is best, and give them a favorable issue for your peace and prosperity.” (All emphases mine). Thomas Jefferson clearly believed that God ruled in the affairs of men, and that a nation could only prosper if its citizens followed His laws.