I've managed to make a timeline for most important events in the story, which should clear out how things happened.
From realistically understanding, original Marina got back to her universe with Rinnosuke somehow surviving as seen him on the hospital bed, still alive and then reaching out to Marina through the time vortex.
As to new now corrected universe, reason why Rinnosuke has wait 3 years for his illness to be cleared is most likely he didn't want to put Marina through painful moments of his illness and death in original timeline.
Anyway, good 9/10 story, would be a whole lot better without the fanservice but I'm sure it's what kept it afloat for so long.
It's basically about a guy who never really knew about being loved a part his early 3 years of life. Rinnosuke never really experienced that basic feeling and was unable to share one right until his death, even though he was married before it was just "siblings love" by a person who was twisted by guilt, guilt of trying to pose as his lost sister that was adopted.