Yes, you would need to adjust for that. Might be the explanation for why the guys from the future shows up in spaceships. I guess it would be dangerous calculating slightly wrong and instead end up inside earth or inside a building's wall.

Better to appear some distance out into space and then fly the last few hundred miles to earth.

The galaxy is rotating and moving through space. All estimated speeds are in relation to other objects.

I think relativity makes this impossible; you're essentially saying there's a particular trajectory that has an absolute velocity of zero. Relativity is founded on the idea that there's no such thing; any trajectory has an equal claim to be the zero velocity.

Maybe time travel would stay in the same reference frame, so if you're on the Earth's surface you end up in the same position on the Earth. On the other hand if you're on an object that experiences non-gravitational directional changes in the span of your time travel, you might be in trouble.

that presumes something like 'time teleportation'. Time travel based on changing / reversing your 'speed of time' doesn't have that.

Kind of like the difference between wormhole based FTL and warp drive based FTL. In one, you just teleport, in the other, you still travel in a continuous line.

This is how I've always imagined a fictional time machine working. You build the thing, it creates a field inside itself, and you can use it to move whoever/whatever is inside that field to other points in the timeline of the machine's existence.