To know what is going on - with respect to MN law - you really need to have a MN lawyer who practices in the area explain things. The media is going to be all about spinning things, and I wouldn't be surprised if they did not understand the law and did not care.
Other than having taken the time to read the parts of the Texas Penal Code that applies to justification of the use of deadly force, I don't claim any particular professional expertise on the subject. If you want to shoot people in Texas, consult a lawyer. With that major caveat . . .
In Texas, justification is all about your fear of being killed or badly hurt being reasonable. The Castle Doctrine says your fear is PRESUMED to be reasonable under certain circumstances - one of which is a break in to your home. So if the State fails to convince a jury (beyond a reasonable doubt) that there was no break in (or something else that triggers the Castle Doctrine) your fear was reasonble and the use of deadly force justified (not quite, there are other things, but close enough).
HOWEVER, if the judge is satisfied that the EVIDENCE AS A WHOLE would preclude the finding that the fear was reasonable, he doesn't submit the issue to the jury. No Castle Doctrine.
So, with the MN facts, I can't see how a judge would ever submit the Castle Doctrine facts to the jury for the actual killing of the girl. The guy wasn't afraid of anything. It's called murder. He would be convicted - even in Texas.
Again, if you live in Texas and really want to understand this stuff, I'd go talk to a lawyer. When you walk out, make sure you have gone over more than the parts of justification and the Castle Doctrine that interest you. You need to understand what a defense is and what a presumption is. And maybe more.
In MN, who knows? But I wouldn't rely on Good Morning America's legal expert or Nancy Grace.