Where to begin. There are a lot of questions or subtopics, in this topic. I don't think I will fully engage this one, but will toss a few thoughts in.
First off, dogs, swine etc, Whether you see them that way or not, is not really relevant. Each one of us rebels against God, and each one of us commits evil and deserves nothing good from God or His people. Apart from God's actions, we would all go to Hell, which is what we deserve.
However, we do not share good things with people because they deserve it, instead they can receive actions of love and grace, because of their great need, and God is merciful and loves the world enough to send His Son to die for us. All believers are commanded to share the Gospel with all who will listen.
End of thought one.
Mysteries are things formerly hidden, now revealed. Mysteries are not secret, hidden things, they are revealed things. Chances are that you know nothing, that has not been publicized. The bible is a publshed (made public) work, a record of what God want's mankind to know about Him and His love and His plan.
Secrets, are something else, mysteries are former secrets. Are there secrets? Sure, and we cannot reveal those, because we do not know them, that is what makes them secrets. Some of these secrets are secrets for some people, and are mysteries (having been revealed) to others, or secrets for some time to be mysteries (revealed) in the future.
End of second thought.
God is capable of keeping secrets and even the secrets for some ears, are revealed to others. Unbelievers do not have God's Spirit, and it is impossible for those without the Spirit, to understand the things of God, they are Spiritually (not intellectually) discerned. You can speak the most critical message in the world (the Gospel) to an unbeliever until you are blue in the face, and although He might understand what your words mean, he will not understand with his heart, unless God has chosen that person, to receive His truths.
Not all are chosen. Some will balk at my Calvinism showing, but this is just Bible, not some doctrine of men. Men's hearts are hardened, only God can soften them. Therefore, you need not worry about revealing secrets, God can keep them even if you are a blabbermouth.
End of thought three, and probably my final thought for this thread. but I may be back, who can say?