Da Vinci was earning a living by painting what the punters wanted. I don't think you can draw any conclusions about his belief system from that. I know very little about him, but Googling "da Vinci beliefs" threw up this:
"Marco Rosci's biography, Leonardo, notes that Leonardo "adopted an empirical approach to every thought, opinion, and action and accepted no truth unless verified or verifiable, whether related to natural phenomena, human behavior, or social activities" http://www.straightdope.com/columns/read/1697/was-leonardo-da-vinci-religious). Leonardo himself wrote, “Anyone who conducts an argument by appealing to authority is not using his intelligence; he is just using his memory.”
Truly, Leonardo valued reason much more than faith. Reason-based beliefs are discovered and verified through the scientific method. The scientific method is when one observes reality with one's five senses, makes logical hypotheses based on one's observation, and then does experiments to prove or disprove one's hypotheses. The vast majority of Leonardo's writings are concerned with observations and experiments. Da Vinci was a great artist, but he might have been a much greater scientist. Judging from his writings, his main goal in life was to know as much about the real universe as he could."
And here are some of Leonardo's own words on the subject (I hope this is allowed, Beth, since you raised the question of whether you have to believe in something to paint it): "Those who try to censor knowledge do harm to both knowledge and love, because love is the offspring of knowledge, and the passion of love grows in proportion to the certainty of knowledge. The more we know about nature, the more we can be certain of what we know, and so the more love we can feel for nature as a whole."
"Of what use are those who try to restrict what we know to only those things that are easy to comprehend, often because they themselves are not inclined to learn more about a particular subject, like the subject of the human body."
"And yet they want to comprehend the mind of God, talking about it as though they had already dissected it into parts. Still they remain unaware of their own bodies, of the realities of their surroundings, and even unaware of their own stupidity."
"Along with the scholars, they despise the mathematical sciences, which are the only true sources of information about those things which they claim to know so much about. Instead they talk about miracles and write about things that nobody could ever know, things that cannot be proven by any evidence in nature."
"It seems to me that all studies are vain and full of errors unless they are based on experience and can be tested by experiment, in other words, they can be demonstrated to our senses."
......
As for people parodying, copying, profiting from or mocking him, I've seen the first three of those, which are to be expected. I haven't seen anybody mocking him but in my opinion anybody who did would have to be as great an idiot as he was a genius.
I'm pretty sure he would not have any problems with being copied; after all. a copy of the Mona Lisa, apparently made by a student looking over his shoulder as he was painting the original, has recently surfaced in Italy. In his day, mass reproduction of originals was not possible and any hand-made copies would be lacking in quality and so would not affect his ability to earn from his art.
To a considerable extent, there is a "seek and you shall find" element in looking for mysterious meanings in ancient, complex artworks. We are programmed to find patterns and meanings so we do it whether or not they are really there. And why would da Vinci want to hide secret codes in a painting? A hidden joke or two might amuse him, or perhaps a theological comment which only the educated would spot - but organising objects on a table to create a piece of music seems really far-fetched. I'm sure Leonardo would despise the mysticism being woven around his work by the likes of Dan Brown.
