So the question is in the title. When I pose characters with livelink it's very easy and intuitive but when I break connection they go back into t-pose. Is there any way to save poses and transfer them in Unreal or save them directly in Unreal?

You can use the sequence recorder in Unreal and "record" the pose, essentially saving it as an animation. You'd just have to name it something along the line of sitting_pose or leaning_pose or whatever the pose is supposed to be. If you were planning to use them as static poses then you'd just drop the pose into the scene and exclude it from your sequencer timeline.