"Does one fly under the hood and the other is the safety pilot both log the time and split the cost in half?"

That is correct.

"What about insurance and getting checked out in the plane."

You're best bet is to do your multi at a place that will let you use the plane for timebuilding. Let's say they require 20 hours to rent. You could spend that whole time getting your ME and then meet the reqs for their insurance. It's a costly way to do it, but a school that trains you and has worked with you often gets you a break on the insurance. But, yeah, the insurance thing can be a problem. If you need 25 multi to meet the insurance mins, you'll need to do that dual before you can timebuild.