You can only ask someone to become your vassal if you are not a vassal yourself. They can either voluntarily become your vassal through a trade agreement (because you are more powerful and they want protection- they also usually have to like you a little), which can be broken (only by the vassal, not by the master), or they can capitulate (surrender) at the end of a war, which is permanent (except they can break away if they reach 50% of your population and land or if you demand a resource of theirs and they refuse- either case results in war between you two). Hope that's not too basic for you.
You can only ask someone to change religion to your state religion, and they must have it in at least one of their cities. They are more likely to change to a religion that they have more of, or that they have the holy city to.
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