Well, since no one bothered to create a savepoint, we can't travel back in time anyway.

did you travel millions of years into the past?

Ahummm, well actually, * adjusts monocle * time travel is not possible and since nobody has invented time machines yet, neither of these scenarios would happen in reality.

So either we would have to invent teleportation along with time travel/ have some sort of "magnet pad' that must exist and not break at all times on earth, or its the time machine type where it just fast forwards everything around you until somehow you're in a mall

I'd like to believe that mass (and then by extension the Earth) "defines" the spacetime around it as much as it distorts spacetime near it. I suspect this may even be the underlying cause for the observation of speed of light being constant in the presence of earth/solar/galactic movement.

I once saw a short film where this was taken into account: they moved back in time a few hours and ended you a few miles away too

This is why you have to calibrate your time machine to track the relative gravity well.

That's why you need a T.A.R.D.I.S.

Nah. Location is relative.

It’s my belief that Time Machines aren’t immune to the effects of gravity. When time changes, the machine goes to the space it would be at if it was affect gravity for the whole time.