I'm going to respond to individual parts of your post.
I think it'd be proper to honor people who is called with such calling and have equipped themselves with seminarian study to serve God's flock.
This is entirely subjective. Though you find it proper, some may not. If a user wants to be called "The Reverend so-and-so" then they can make their name say exactly that. They can further clarify that they are indeed a Reverend in their profile if they wish.
Would it be possible for an ordained minister to get a unique title or special badge to honor their privilege.
I don't believe it would be possible or supported by the SE staff. Some sites do have custom badges, but they are related to achievements on the site. There's also a problem of verification. How would we do that? I don't really feel like calling seminaries to be sure certain users completed with good standing. But unless it's verified, then it is meaningless.
This would also clarify whether or not their answer is credible in case an ordained minister from one group of belief is trying to answer a question about another group of belief. I personally would prefer an answer from a Baptist minister to answer a particular question about Baptist faith rather than from a non-Baptist guessing and quoting what a Baptist might believed.
You might personally prefer an answer from a Baptist minister for a Baptist question, but concluding that such answers are automatically better based off that single criterion is a combination of logical fallacies. Specifically, it is an appeal to authority and a genetic fallacy. This community would be remiss to devise a system that propagates any logical fallacy. This is, therefore, not a supporting point of your proposal, but rather a supporting point of a rebuttal.
I hope we can have an option to specify if a person is an ordained clergy to honor them with an honor due to them.
SE already has a system that brings users "an honor due to them" and it is entirely based off of the quality of answers and question that you post. "Let your work speak for itself" is the crux of this model and does not bother with considering any real life laurels you might have. For as faith without fruit is dead so also is an education not put into practice or shared.
When we're having multiple opinions it'd be helpful to have a clergy explaining the official teaching. An example would be from Puritan Board where you can see whether or not you're talking with a laity or a clergy.
I'm afraid I don't see how this is helpful. This harkens back to the previously used logical fallacy. Additionally, I prefer to "Let the work speak for itself" and I would bet a good deal of the users already here agree. We'll see in the votes on this post.
Summary: There's no apparent benefit to the site or it's users given in your post or otherwise.