Is it ethical to apply to a scholarship sponsored by my employer?
"I contacted the communications department via e-mail and asked if it is illegal and/or unethical to apply. Response said that company employees can apply, which means, I can apply."


I think that answers the ethics about it as well. As long as you are open about the fact that you are a company employee, there is no scope for you to violate any ethics. Any possible violation (which I don't think there are any) would be in the company's hands.

Think about this - why is the company offering a scholarship? They probably want the recipient to graduate and then work for the company. Thus by attracting top students to apply for an attractive scholarship, they gain a highly skilled and motivated employee. Sure, the fact that you already work for them might give you an advantage in the application process. But this is a private company giving out privately earned funding. They should be able to pay whomever they choose, for whatever reason.

In the end, there is really little difference between this, and an internal hire.