Does my carrier charge me extra if I turn on "Send as SMS" option?

It should not charge you if you are on AT&T, Verizon, or Sprint. These cellular carriers require a basic plan that includes UNLIMITED texting on all smartphones so it should not charge you extra. Clicking "Send as SMS" simply just sends it as a text message in the case that your 3G or LTE is not functioning properly.

If you are using imessage that goes through wi-fi or cellular, therfore, it will going through data and charging you for data. Its a very small amount of data like KB small but its still charging data if its over cellular

That because if you didn't have unlimited and you went over, it would charge you. As far as you having Unlimited, you have no worry about it being on

If its sending as an iMessage, it will be using Data

if it sends as an iMessage, its data, if it sends as a ams it is texting

No. It will not count as using data. It will send the messeage as a text message.