How does space exploration contribute to global warming?

To answer the title question, spacecraft launches (with a rocket) are incredibly energy-intensive and most of that is fossil-fuel energy, so there's a lot of CO2 right there.

But without satellites showing us what is going on on our planet as a whole, and without some explorations of other worlds to compare ours to, we'd have a much worse grasp of the problem.

Think of the technology that's been created because of space exploration. Had we not spent that much money sending rockets into space, and burning all that oil, we wouldn't be driving electric cars, or saving lives with hospital equipment. Space exploration expands our technology, and this in turn cleans up the environment.

The question presumes global warming is real and a result of human activity.  Since the scientific method demands that hypotheses be falsifiable, and MMGW can't be falsified, that's an invalid assumption.  When MMGW makes a prediction unique to human caused climate warming, and that prediction is confirmed, get back to us.

it is insignificant
space exploration is not to blame
global warming may be a natural cycle we have no control over

Go to the NASA website, on the home page you will find the connections to the sub site(s) that will answer your questions

It contributes by showing that all planets have cycles of warmer & colder weather.
1.  By helping us understand our atmosphere & the reactions of our environment to the sun,
2.  It has made people smarter and provided advanced technologies in the past and present.
3.  By letting us see what is happening on other planets and by giving us an outside, global view of Earth.
4.  Sure.  The smaller the scale, the more influence we have.  Very large scale changes are debatable.
5.  We may find a way today but not be able to enact it until the future.