https://iextrading.com/ obviously offers trading services but when I look for an API, I keep getting shunted off to the data feed APIs. No order API is anywhere in sight. Am I missing something?
Then what does this quote from their website mean?
They are an exchange, not a broker. Your broker has the option of routing trades thru IEX for actual execution.

And why would you tell him that?
(if he can't figure out this much then what chances of survival does he have)
I wonder how many people die because they are too ashamed of their ignorance to ask ignorant questions?
But then, I suppose you think you're doing Darwin's Work, right?
It's not the question, it's the answer. One that doesn't help you think on your own. This can be more dangerous than asking ignorant questions because you'll keep asking them.