I see. So the way that john titor explained it isn't exactly how your people actually believe time travel works? According to titor, from what I can gather, travel to other worldlines is not really time travel - it is just traveling to co-existing realities that happen to resemble the past or future of another worldline.

No, Titor was correct. If you're purposefully traveling to another world line that is not time travel. But if you are traveling specifically to the past it is hard to know what world line you may end up in. For all I know, some of my colleagues could have ended up in this world line.

When your people have sent others into the past to fix some event, have you ever seen the results propagate up the timeline "instantly"? Like say you and one of your colleagues swapped roles, where you stay in your original worldline in 2036 and your colleague travels to this worldline where it is 2015, and guides the young boy to a healthy lifestyle. Assuming that the worldlines crossed, what would you experience? Would you remember sending your colleague back in time? Would the very important man have ever had the health issues that prompted the mission, or would he be very healthy and fit and thus the mission never needed to happen?

You would need a god's eye of the world to see changes. Otherwise the timeline corrects itself and nobody will notice any difference except for the person who changed it.

Would you be willing to share the story about the possible ghost, even if it is silly? I'm very interested in this subject and in hearing peoples' personal experiences.

For a short time when I was a kid I lived in a traditional Japanese house (Renovated to be a bit more modern) in a small village in Kyushu. One night I had awoken and thought I had seen a faceless figure floating above my futon. It disappeared when I began to scream for my parents and I have never seen anything like it since.