Let's call the time interval of washing the windows in the train's reference frame $\Delta t$ and the time interval in the stations reference frame $\Delta t'$. As you alude to, the observers at the train station will measure this time interval to be longer than those on the train, specifically $\Delta t' = \Delta t \gamma$ where $\gamma > 1$ when the relative motion is not $0$.
This essentially means that the time interval that would pass from the person on the train started washing his windows till he ended would seem longer from the perspective of the observer on the station. The closer to the speed of light he is moving at, the slower he would seem to be moving.
As a more illustrative example, consider the following:
Lightning strikes the end of a moving train car. The train car has a length of L. To an observer located at the other end of the train car, the flash will reach him at the time,
$$ t = \frac{L}{c} $$
where $c$ is the speed of light, which is always the same for all observers in relativity. For an observer on the ground though, the train will have moved slightly between the two events, meaning that the light flash will have traveled a slightly different distance. This distance could be longer or shorter depending on the direction of the trains movement. Let's call this change in distance $\Delta L$. We then get the time as measured in the ground reference frame
$$t' = \frac{L+\Delta L}{c}$$
which illustrates that, if the speed of light is the same for all observers, the time it takes light to travel the length of the train is different for the two observers. This is analogous to your example of washing windows, except instead of the train moving slow compared to $c$ and the movement inside the train (lightning flash) being close to $c$, the situation is reversed (train speed close to $c$, speed of washing hands not close to $c$).
The important thing to remember here is that special relativity only works on inertial reference frames (i.e. no acceleration), so the two observers could never meet to compare clocks, except for possibly one single occasion when they pass each other (which is generally considered the point where $t = t' = 0$). This means there is no "true time" in special relativity. They are both correct in their analysis, even though they would disagree on the time interval if they could meet which, again, they can't unless one of them accelerates. (In the case of acceleration, general relativity would be required to analyze the scenario, which I am not familiar with... although I know time is still funky. There is no absolute time).
Length contraction is entirely reciprocal between two inertial frames. If you are moving relative to me, and lengths in your frame seem to me to be shortened by 10%, say, then lengths in my frame will appear to you to be shortened by 10%.
Time dilation is reciprocal in the same way. Suppose four minutes pass on your watch while you coast between two events in my frame, and the time difference between those two events in my frame is five minutes. Given that, while four minutes pass on my watch I will coast between to events that are five minutes apart in your frame.
The twin paradox is another effect altogether, and is asymmetric.
Best Answer
Although mathematically allowed, the limiting case where the massive object reaches the speed of light is not practically realizable. This is often the situation with scenarios found in special and general relativity. There are limits that can never be reached in the physical world. A massive object reaching the speed of light is one such case.
Also remember the length contraction and increase in mass are relative observations. For the person inside the space ship, the length and mass remains the same. It's only the external observer that looks at the space ship speeding past it (i.e., a transverse observer as Steve explained) that will observe the length contraction.