Is There A Way To Successfully Send A Text Without Knowing The Provider?

Well if you mean by provider is the cell phone company of your friend then you can't send a message to your friend until you know the provider. There can be many same numbers with different service providers so you need to know the exact provider.

I guess I don't know what a texting site is, free or otherwise.  You can send a text on your cell phone to anyone with a cell phone whose phone number you know.  I can't imagine why you'd need to know the provider if you are simply sending cell phone to cell phone.  I suspect that is not what you mean though, so my answer is probably no help whatsoever.   There certainly are not "many same numbers with different service providers" in the US.

Yes.  You can text without knowing the provider at SMS Everywhere.  It's free up to 150 characters.