You have a few options on how to deal with this type of behavior.
Ignore the user
It sounds like some of your admins are already taking this route. Your admins are under no obligation to answer personal questions or engage in topics outside of their role as part of the community. By ignoring the unwanted behavior, the user has already learned that some topics will be ignored. Repeatedly ignore the engagements and they will learn to stop. Of course, a simple reminder that a topic is to personal or that they don't wish to engage with the user about a topic isn't uncalled for either. After that reminder, ignore further attempts to engage in those private conversations.
Firmly state that the behavior is unwanted
Ignoring may be a subtly the user doesn't understand. It's also not the best practice to go around ignoring your community members. An alternative is to very clearly state that admins will not engage in private conversations that are of a personal nature or that don't involve their role as a community member. You can have each admin that the user engages with issue this disclaimer or you could post it publicly. If you go with the latter option, you don't need to call the user out by name. Make it a new policy for the entire community and encourage discussion publicly.
Encourage engagement with the community
While the user may prefer the private conversations, you need to steer that desire to talk and communicate toward more appropriate venues. When the user asks a question, try and relate it to another area in the community. Provide links to those discussion areas and encourage them to engage. Don't provide links to a general forum, but instead to very specific threads. Use their interests to pull them back toward public conversation. If your community feels it's appropriate, tag the user in an on going conversion where they have expressed interest and ask for their opinion or feedback. If they don't wish to engage publicly, then they won't. But, that is where they should be talking and not bothering your team with unrelated conversion.
Don't engage in community discussions in a private venue
The discussions that are clearly oriented toward the community or decisions made by the admin team should take place in the appropriate venue as well. If the user is asking why certain decisions were made, that sounds like something the entire community could benefit from knowing. If your team discusses that kind of topic publicly, answer it publicly but only after it's been posted publicly. If the user is asking about a topic that your team won't answer publicly, state that and end the conversation on the topic. If they want answers and it is related to the community, the topic should be available to the community. Don't fragment your team by discussing community actions both in public and private. If you are striving for an open dialog, community members should be doing the same.