The Eilenach beacon was originally built to communicate with Gondor's northern defenders in Calenardhon, so it must logically have been put in place before Calenardhon was granted to the Rohirrim in III 2510. That land had been deserted for some time beforehand, and so the Eilenach beacon probably dates from several centuries before the establishment of Rohan.
2
This pronunciation is based on Elvish rules, but the name Eilenach is specifically said not to be Elvish in origin, so those rules may not apply in this case.