With the Space X success at re-using rockets, my thought is that the second stage could be refueled at the ISS. Similarly, fuel could be sent to orbit Mars. My thought is it would allow for greater acceleration and therefore cut travel time.
SpaceX's intent is to use orbital refueling to allow Starship to reach destinations beyond low Earth orbit. However, these plans simply involve meeting up directly with the tanker to transfer propellant.
The ISS has no facilities for storing or transferring the liquid methane and oxygen Starship uses as propellant. If it did, you'd still need two separate rendezvous and docking operations when directly meeting with the tanker only requires one. And finally, the ISS is in a fairly highly inclined orbit. Not only would this limit the payload the Starships could carry, it wouldn't necessarily line up with your intended destination.
The point from the Earth orbit from where we launch has little influence on the travel time. Currently all missions to Mars use the less energetic path. Basically, we accelerate the spacecraft until we reach an elliptical transfer orbit around the Sun with the periapsis (closes point to the sun) in Earth Orbit and the apoapsis (further point from the sun) intersecting Mars orbit. Once in that that trajectory the spacecraft coasts the rest of the way, braking once it reaches Mars's sphere of influence. This is the best you can get with current technologies and takes around 259 days, about 8.5 month, and most missions have barely enough fuel to perform this maneuvers, most Martian Rovers don't even use fuel to break, instead perform an aerobreak maneuver in Mars atmosphere. The only option to cut that time is to accelerate during extended periods of time during the first half of the trip and break during the same amount of time during the second half. We can't do that yet, and definitely not with chemical rockets, although some ion and plasma engines (some already in prototype and demonstration stage) have the theoretical capacity to reduce the trip to 2 months. Starship is designed to use the first approach and it will be limited to the less energetic path, so refueling in the ISS or refueling using a tanker makes little to no difference to the travel time, is completely limited to that specific transfer orbit. Added to this, the ISS has no infrastructure for refueling or storage and given the complexity of the structure it would be incredibly expensive to implement something like that, specially compared to use a reusable tanker from SpaceX.