A question to consider however is: How would, assuming it is possible, time travel affect the linear reality? What is the effect of a modern day human travelling back in time, will he/she be the cause of countless terrible (modern anno 2017) illnesses. Better yet will he/she die from the sudden non existance of the previous time passed, growing up etc, or is this somehow irrelative, does this time "travel with the person"?

The problem with time travel is that, space and time are Relative.
Their relativity might not be completely bound together though, which is why travel between the Infinite amount of alternate realities is more likely, at least in my humble uninformed, but well read, opinion.