How does chewing gum affect the ears? I heard that it improves your ear health. Is this true?

No. In fact excessive chewing can cause temromandibular joint pain in some patients which can cause pain in front of the ear.
Not true. In general, probably doesn't hurt, but surely doesn't help. It can help equalize ear pressure on a plane flight as chewing and swallowing can help open the eustachian tube. I do see a fair number of patients who get ear aches from TMJ caused by gum chewing, though. Enjoy your gum, but certainly don't do it to "improve your ear health." best wishes!