My mother was detected with ascending aortic aneurysm of 3.9 cm in april 2013. will she be able to fly internationally?

Yes: Normal is up to 3.6 cm. Her 3.9 aa is very small. Get it checked annually. Bon voyage!

Yes: As long as she has no significant aortic valvular heart disease, and no chest pains or other unexplained symptoms, she should be fine. I wouldn't worry about the aneurysm ( again as a sole problem) unless it were at least 4.5 cm. Make sure she gets follow up for it though.