Questions about Lines of Simultaneity

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Suppose you are using 2-D spacetime diagrams in which the vertical axis represents time and the horizontal axis represents space, and you have two observers, one who is always stationary and one who can move. Then, going from being stationary to the speed of light, is it true that the line of simultaneity for the moving observer goes from horizontal to 45 degrees to the origin? Also, is c the only velocity for which the line of simultaneity is the same as the worldine of the moving observer? Finally, is it true that lines of simultaneity don?t exist for the moving observer when he is going at velocities greater than c?

Thanks for any help!

PS: This is addressed to certain persons who seem to think it's rude to post questions involving time travel physics jargon to a public board such as this without explaining every little term. I
am posting questions here because there are a lot of things I don't know and I would like to get more information on. In the same manner, if someone doesn't know what I'm talking about, they should try posting questions and/or try reading one of the (right now, few) books out there pertaining to time travel that doesn't involve detailed knowledge of physics. I have no way of knowing exactly what visitors to this board know and don't know. Furthermore, even the little that I do know is not particularly easy to explain to others, especially without diagrams, which is where the books out there would come in handy. Despite the fact that I usually visit this site several times a day, I'm not quite sure what a hyperdimensional resonator is. Does that mean I go around griping to people that they haven't spelled out everything to my satisfaction? No. If I really wanted to learn about hyperdimensional resonators, I would use search engines to visit different sites regarding this device, read postings, ask questions, etc. Likewise, I think others should do the same if they really want to learn about certain things.