“Are massages safe during the third trimester?”

Massages are perfectly safe. However Be sure your massage therapist knows that s/he is not to massage your Achilles tendon. Doing so will bring on labor/miscarriage. The Achilles heel/tendon/ is related directly to the reproductive organs. That area, just behind the ankle, is wonderful when you are menstruating and experiencing cramps. Then massaging both sides of the tendon, just behind the ankle, will help to alleviate those cramps.
Also, be sure to avoid lieing on your back, and of course, not lieing on your stomach during a massage. Lieing on your sides, particularly your left side, will be the best postures for the embryo. Congratulations!

Yes massage is ok at that time frame.