i’m probably missing something, but i don’t really get the purpose of this in the first place.
after all, what you’d need to do is
a) select items
b) go to orderpage and fill in info
c) submit order
which does all the scripting inserting order, sending emails etc etc
so why not use what you have (i.e the website) to do this instead of building the same thing twice ?!
in any case, there’s no “API” or whatever it is you want to call it.
there are filters, actions and shortcodes you can use to do things….