Yes. The short answer is that exercise is a beneficial activity throughout pregnancy and virtually all pregnant women should exercise. Almost every limitation to exercise that you heard or read elsewhere on the Internet is not based in science. Women who exercise have better pregnancies in every aspect.
Read more about exercise during pregnancy here.
In general, the answer is yes.
There is nothing inherently dangerous about traveling by ground, sea, or plane during pregnancy. However, you do have to consider how long you will be separated from the ability to seek medical care, and how far away that medical care might be. This is more important in the third trimester, particularly in the late third trimester when labor is more likely. For this reason, mini cruise ships will not allow you to embark after 24 weeks because they do not want any liability related to premature delivery when the baby has a chance at viability. It’s not that sailing isn’t safe, it’s only that it is many hours away from hospital.
Planes do not often limit travel by gestational age, but you should consider how long your flight is. There is a big difference between flying from Atlanta to New York versus flying from New York to Melbourne. In general, many doctors recommend avoiding flying after 35 weeks if the length of the flight is particularly long.
Some people worry about travel by car due to the concern of increased risk of blood clots secondary to the immobilization. This is probably not a valid reason to not travel by car, particularly when you consider that pregnant women will be forcing pit stops every two or three hours anyway. When you stop for a potty break, be sure to walk around for a couple of minutes.