I think you're mixing apples and oranges here, MJ. A defintion of "completed application" is necessary so you know when the 30 day clock starts ticking for having the provide an adverse action notice, among other things. But one can have an "application for credit" long before one has a "completed application." In your case, for instance, you automatically have an application for credit when you've obtained a credit report, thus triggering all the requirements of Reg B.
And no, you can deny credit long before you have a "completed application." If credit is bad, the app is dead right there, no need to complete the app. If credit is good but income is insufficient, again, no need to go futher, right? But you've still got an application and have to do all the Reg B required steps (notice, record retention, government monitoring information, etc.)
And no again, most shops pull credit first thing but it's purely a matter of your shop's procedure. (And FWIW, I like you shop's policy that credit report = application. Too many people would like to say, "Well, I pulled the customer's credit and after the customer saw his or her credit score, they 'decided not to proceed' so I don't have to treat this as an application." All kinds of potential trouble lurks behind that statement.)
Good luck out there.
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The opinions expressed are mine and not those of my employer