If a married man was to have an affair with a woman and she gets pregnant, is the man responsible for paying child support for that child?

It makes no difference if he is married or single. If he is the father he is obligated to pay.

Why would you think otherwise? You stick it where it don't belong and you pay the price.

They are only responsible till the child turns 18 unless the child goes to college.

Yes, the man is always responsible, being married or not makes no difference. The court will order DNA tests, and allow the man visitation rights ( unless there is a reason not to ) and set the state required child support

Yes, if he is proven to be the biological father, he is responsible to support the child he made. Doesn't matter if he's married to someone else or not... if you make a child, you have to take care of it.