1) Time. There's a main effect of time. There are one or more pairs among the levels that are significantly different from one another (although you could have a main effect and none of the pairs are different).
Time * group is the test of interaction. One simple way to describe is that the differences between the experimental and control groups are unequal at each level of the time variable. So the difference between experimental and control is different in the pre-test than the post-test. That's just one outcome though. There may be others.
The between-subjects test result means that when you compare the mean for the experimental to the mean for controls, hey are not different.
Typically you should interpret the interaction over the main effects especially when they are disordinal. That is, one level is higher across some or one levels of the other variable and equal or lower across the other(s).
2) If I recall correctly, you can usually ignore the Intercept, which tests whether the grand mean is = zero.
3) I don't know what software you're using so I have no idea.in SPSS you could set up contrasts.