Well, of course, in a sense he worked for money. He was employed as a musician. He had to make a living by accepting commissions for his work.
However, if you knew anything at all about Mozart, you'd know that 1) the movie Amadeus is a completely inaccurate representation of him, even bordering on character assassination 2) that he wrote music because he has entirely taken up with music. He loved composing, and we can see this by the fact that some of his greatest works weren't even commissioned (e.g., Mass in C minor).
I've read three biographies of Mozart and a good number of his letters, and from all of them there is a very apparent indication of Mozart's religiosity.
Here are some excerpts from his letters:
As death, when we come to consider it closely, is the true goal of our existence, I have formed during the last few years such close relationships with this best and truest friend of mankind that death's image is not only no longer terrifying to me, but is indeed very soothing and consoling, and I thank my God for graciously granting me the opportunity...of learning that death is the key which unlocks the door to our true happiness. I never lie down at night without reflecting that —- young as I am — I may not live to see another day. Yet no one of all my acquaintances could say that in company I am morose or disgruntled.
I know myself, and I have such a sense of religion that I shall never do anything which I would not do before the whole world; but I am alarmed at the very thoughts of being in the society of people, during my journey, whose mode of thinking is so entirely different from mine (and from that of all good people). But of course they must do as they please. I have no heart to travel with them, nor could I enjoy one pleasant hour, nor know what to talk about; for, in short, I have no great confidence in them. Friends who have no religion cannot be long our friends.
- Letter to Leopold Mozart (1787-04-04), from The Mozart-Da Ponte Operas by Andrew Steptoe [Oxford University Press, 1988, ISBN 0-198-16221-9], p. 84
- Letter to Leopold Mozart (Mannheim, 1778-02-02), from The letters of Wolfgang Amadeus Mozart, 1769-1791, translated, from the collection of Ludwig Nohl, by Lady [Grace] Wallace (Oxford University Press, 1865, digitized 2006) vol. I, # 91 (p. 164) 
- God is ever before my eyes. I realize His omnipotence and I fear His anger; but I also recognize His love, His compassion, and His tenderness toward His creatures. He will never forsake His own. If it is according to His will, so let it be according to mine. Thus all will be well and I must needs be happy and contented. (Letter of 25 October, 1777)
- In those distressing circumstances [Mozart is referring to his mother's death], there were three things that consoled me, namely, my complete and confident acceptance of God's will and the presence of so easy and beautiful a death, which made me think that in an instant she had become so happy - how much happier she is now than we are, so that at that instant I wanted to make the journey with her. - This wish and this desire provided me with my third source of comfort, namely, that she isn't lost forever - that we shall see her again - that we shall live together more happily and more contentedly than in this world of ours. (Letter of 9 July, 1778)
"I will see you in a better world--and never to part." - September 3, 1787. Mozart's entry in his private album, in reference to his doctor, Sigmund Barisani, who had recently died.
- Don't worry about the good of my soul, most beloved father! I'm just as likely to err as any other young man and by way of consolation wish only that others were as little likely to err as I am. You may perhaps believe things about me that aren't true; my main failing is that I don't always appear to act as I should.-It's not true that I boasted that I eat meat on all fast days; but I did say that I set little store by it and don't consider it a sin; for me, fasting means abstaining and eating less than usual. I attend Mass every Sunday and feast day, and, if I can make it, on weekdays too, but you already know that, father. (Letter of 13 June, 1781)