Dependent Visa for Kids, 10 and 14 y/o

Hi,
I am planning to get my kids here in Indonesia this coming school year 2015-2016. I am currently working in a school here in Surabaya, on my second year.
With this, I know that I would need to acquire dependent visa for my kids.
I hope you could help me know the process and possible costs.
Thanks.

The school you are working at should be handling this for you.

The school should do this but, if they don't/won't, the local immigration office should easily be able to handle it.
The KITAS fee for an adult is less than Rp1,000,000, including photos and bits and bobs (if you do it yourself). I think, but am unsure, these fees also apply to dependent children.
Assuming you have a valid KITAS/work permit, it should be pretty smooth.

Could someone advise how long the dependents' visa processing usually take?

Thank you!

Just be aware that some Islamic countries do not provide dependents passes, unless the mother is married and living with the father of the children.