The problem comes in due to relativity. Mars and Earth (and other planetoids) travel at different speeds. The very length of a second will drift over time.
No. You would have to observe the planet from your position and that observation changes based on how you move relative to the planet. The whole of SRT and GRT work in such a way that no general clock synchronization can ever exist for observers in different frames of reference.
If you take a reference with you on a journey through the solar system, that reference will stay accurate for an observer travelling with it and drift as seen from an observer that stayed behind. Both views are accurate. Locally, the amount of time that has passed for each observer was different. If you would correct for any observed drift, you would mess with your fundamental unit of time in your local frame of reference and get incorrect measures of time passed in your own frame.
What I had in mind is, you can observe your planet's position and velocity (relative e.g. to center/rotation of the galaxy), and the target planet's relative position and velocity, and use both to translate the observations into virtual "stationary" observations... And "unit of time" would be defined as 1/n of one planetary/galactic revolution, so every observer would be able to calculate their own "galactic time" independently. Well, maybe GPS already does something similar.
No, you can't. Atomic clocks measure the oscillation of atoms (I think Cesium is currently used), and though constant at a fixed point, vary when theyre moving at different speeds. GPS wouldn't be possible without taking this into account, for example. A second on earth will never be the same as a second on Mars.
A second is duration, but we're really interested in instants. Why can't you can define an instant independently of the observers, e.g. in reference to the rotation of the galaxy (i.e. "this happened at angle 37 from Milky Way - Andromeda line, at distance 403 parsecs from Milky Way center, at 692.3 Milky Way rotations since epoch (Big Bang)").